The good thing about Yazid's narration is that it's detailed, which helps us understand what the meaning is as opposed to a vague brief report. The Shia prefer the vague report, as they can give it all sorts of interpretations. Ahlul-Sunnah want the detailed report because they wish to understand what is intended from those words.
Here I quote Zayd's Hadith from Musnad ibn abi Shaybah who died in 235 AH (almost 30 years before Muslim) and it's the same text either-way:
[He (saw) praised God and offered wisdom then said: "To begin, O people I await my Lord's messenger to respond and I am leaving among you two heavy burdens, one of which is God's Book, in it is guidance and light; so hold onto God's book and adhere to it." He (saw) encouraged us to stick to God's Book then said: "And my household; By God I remind you of my household."]
Let us look at the green part, it is quite clear that he never asked anybody to hold on to anything other than God's Book here right? In fact, he (saw) goes out of his way to describe how it guides us towards light.
Now if we read the red part, it's clear these are not Yazid's words or anybody other than Zayd himself, he was narrating what happened and describing the situation. This part further emphasizes that they were being encouraged to hold onto God's book for guidance.
The last blue part, does not state that we must hold onto the household nor that there's any guidance involved, it is a reminder for us to take care of them.
At the end of the narration, notice how Zayd lists the members of the household. Clearly he's not talking about chosen individuals or infallible leaders, he's talking about the paternal relatives (`Abbas's family, Harith's family, `Ali's family, Ja`far's family).
Now why is the Shia on that site going out of his way to authenticate specifically the narration of abu al-Duha? He does it for two reasons:
A- abu al-Duha's report contains "They shall not separate until they reach me at the pond."
Regarding this, we Ahlul-Sunnah have no issue. Although this is a vague statement, yet we can give it a suitable interpretation which is that the Prophet (saw) told us to be responsible for the Qur'an and his household. Being responsible for the Qur'an means learning its guidance, preserving and teaching it. Being responsible for his household means giving them their due rights and protecting them. When a Muslim reaches the pond having done his duties, he is safe. However, a Nasibi such as Hajjaj who taught Qur'an but hurt the household will have a problem at the pond.
B- one of abu al-Duha's reports can be twisted to imply that Ahlul-Bayt offer guidance.
The one familiar with abu al-Duha's reports knows that it does not state anything with regards to acquiring guidance neither from Qur'an or from Ahlul-Bayt.
It simply says this:
أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ، قَالَ: قَالَ رَسُولُ اللَّهِ: إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ كِتَابَ اللَّهِ وَعِتْرَتِي أَهْلَ بَيْتِي، وَإِنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَيَّ الْحَوْضَ
[I am leaving among you two heavy responsibilities, God's Book and my progeny; my household. They shall not separate until they reach me at the pond.]
YET, one report attributed to him has a slight variation:
عَنْ أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ، قَالَ: قَالَ: النَّبِيُّ: إِنِّي تَارِكٌ فِيكُمْ مَا إِنْ تَمَسَّكْتُمْ بِهِ لَنْ تَضِلُّوا كِتَابُ اللَّهِ وَعِتْرَتِي أَهْلُ بَيْتِي، وَأَنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَى الْحَوْضِ
[I am leaving behind a thing that if you hold onto it, you shall not go astray God's Book; and my household. They shall not separate until they reach me at the pond.]
Now we respond to this by saying: We interpret this in the context of Zayd's other more authentic narration, in that the above text is limiting guidance ONLY to the Qur'an. This is why it says "If you hold onto IT you shall not stray God's Book" This part is only referring to the Qur'an thus the singular "It" when referring to the object of guidance. The Prophet (saw) then adds that he is also leaving behind his household. Of course we know this because it's a brief summarized narration, the more detailed reports state how the Prophet (saw) described the Qur'an as a rope from the sky and a light of guidance before moving on to reminding us of his family.
Our second response is a Hadithi one, we say: This report is incorrect, the narrator confused a part from abu Sa`id's narration with Zayd's narration.
The narration reported by the Kufans from abu Sa`id is the one that states in some versions "That if you hold onto it, you shall not go astray" However, abu al-Duha's report from Zayd does not.
To illustrate this, let us collect all of Zayd's reports from abu al-Duha starting with the suspect narration:
حَدَّثَنَا يَحْيَى، قَالَ: حَدَّثَنَا جَرِيرٌ، عَنِ الْحَسَنِ بْنِ عُبَيْدِ اللَّهِ، عَنْ أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ، قَالَ: قَالَ: النَّبِيُّ : " إِنِّي تَارِكٌ فِيكُمْ مَا إِنْ تَمَسَّكْتُمْ بِهِ لَنْ تَضِلُّوا: كِتَابُ اللَّهِ وَعِتْرَتِي أَهْلُ بَيْتِي، وَأَنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَى الْحَوْضِ
وَحَدَّثَنَا يُوسُفُ بْنُ مُوسَى، قَالَ: نا جَرِيرُ بْنُ عَبْدِ الْحَمِيدِ، عَنِ الْحَسَنِ بْنِ عُبَيْدِ اللَّهِ النَّخَعِيِّ، عَنْ مُسْلِمِ بْنِ صُبَيْحٍ، عَنْ زَيْدِ بْنِ أَرْقَمَ رَضِيَ اللَّهُ عَنْهُ، أَنَّ النَّبِيَّ رَضِيَ اللَّهُ عَنْهُ، قَالَ: إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ: كِتَابَ اللَّهِ، وَأَهْلَ بَيْتِي، وَإِنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَيَّ الْحَوْضَ
حَدَّثَنَا مُعَاذُ أَبُو الْمُثَنَّى، ثنا عَلِيُّ بْنُ الْمَدِينِيُّ، ثنا جَرِيرُ بْنُ عَبْدِ الْحَمِيدِ، عَنِ الْحَسَنِ بْنِ عُبَيْدِ اللَّهِ، عَنْ أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ، قَالَ: قَالَ رَسُولُ اللَّهِ : " إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ كِتَابَ اللَّهِ وَعِتْرَتِي أَهْلَ بَيْتِي، وَإِنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَيَّ الْحَوْضَ "، حَدَّثَنَا أَبُو حُصَيْنٍ الْقَاضِي، ثنا الْحِمَّانِيُّ، ثنا جَرِيرُ بْنُ عَبْدِ الْحَمِيدِ، عَنِ الْحَسَنِ بْنِ عُبَيْدِ اللَّهِ، عَنْ أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ، عَنِ النَّبِيِّ مِثْلَهُ
حَدَّثَنَا عَلِيُّ بْنُ عَبْدِ الْعَزِيزِ، ثنا عَمْرُو بْنُ عَوْنٍ الْوَاسِطِيُّ، ثنا خَالِدُ بْنُ عَبْدِ اللَّهِ، عَنِ الْحَسَنِ بْنِ عُبَيْدِ اللَّهِ، عَنْ أَبِي الضُّحَى، عَنْ زَيْدِ بْنِ أَرْقَمَ قَالَ: قَالَ رَسُولُ اللَّهِ : " إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ كِتَابَ اللَّهِ وَعِتْرَتِي أَهْلَ بَيْتِي، وَإِنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَيَّ الْحَوْضَ
حَدَّثَنَا أَبُو بَكْرٍ مُحَمَّدُ بْنُ الْحُسَيْنِ بْنِ مُصْلِحٍ الْفَقِيهُ بِالرِّي، ثنا مُحَمَّدُ بْنُ أَيُّوبَ، ثنا يَحْيَى بْنُ الْمُغِيرَةِ السَّعْدِيُّ، ثنا جَرِيرُ بْنُ عَبْدِ الْحَمِيدِ، عَنِ الْحَسَنِ بْنِ عَبْدِ اللَّهِ النَّخَعِيِّ، عَنْ مُسْلِمِ بْنِ صُبَيْحٍ، عَنْ زَيْدِ بْنِ أَرْقَمَ رَضِيَ اللَّهُ عَنْهُ، قَالَ: قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَآلِهِ وَسَلَّمَ: " إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ: كِتَابَ اللَّهِ، وَأَهْلَ بَيْتِي، وَإِنَّهُمَا لَنْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَيَّ الْحَوْضَ
قَرَأْتُ عَلَى مُحَمَّدِ بْنِ مَسْعُودٍ، ثنا أَبُو حُجْرٍ عَمْرُو بْنُ رَافِعٍ، ثنا جَرِيرٌ، عَنِ الْحَسَنِ، عَنْ مُسْلِمٍ، عَنْ زَيْدِ بْنِ أَرْقَمَ رَضِيَ اللَّهُ عَنْهُ، قَالَ: قَالَ رَسُولُ اللَّهِ : إِنِّي تَارِكٌ فِيكُمُ الثَّقَلَيْنِ: كِتَابُ اللَّهِ، وَأَهْلُ بَيْتِي، وَإِنَّهُمَا لَمْ يَتَفَرَّقَا حَتَّى يَرِدَا عَلَى الْحَوْضِ
Notice how all versions above say "I am leaving behind me al-Thaqalayn" except one version that says "I am leaving behind me what if you hold onto it you will not stray."
A- Jarir bin `Abdul-Hamid and Khalid bin `Abdullah both narrate the report from al-Hasan bin `Ubaydullah.
B- Khalid mentions nothing about guidance in his report. Jarir mentions the guidance version.
C- Jarir doesn't mention guidance in five versions but only mentions it in one version.
Conclusion: It's not possible that five people made a mistake while narrating from Jarir and only this one narrator "Yahya" got it right.
This is a sufficient response, if you wish to go further, try investigating WHO this Yahya is in the first place.