This Hadith has nothing to do with the grave of the Prophet Sallallahu alaihi wasallam. There is no proof that giving Salam near the grave of the Prophet Sallallahu alaihi wasallam is any different than giving Salam to him from afar. The Angels convey the Salam to him in all instances because he has no awareness of anything from this Dunya; nor can he hear anything from this Dunya; nor is he present in his grave in Medina; rather the grave in Medina only contains his bones. (Sallallahu alaihi wasallam).
I'll quote the scholars and let the readers judge.
Shaikh ul-Islaam Ibn Taymiyyah writes: “The scholars have understood [from this hadeeth]
that this salaam [regarding which it is said that Prophet’s soul returns to his body]
is only that which is said near the Prophet’s grave, this hadeeth is not a proof for the one [sending salaam] from far away” [Ar-Radd Ala al-Bakri: 1/107]
He further said: “This is the hadeeth upon which the Scholars like Ahmed and Abu Dawood trusted on the issue of saying
salaam from near the Prophet’s grave.” [Ar-Radd Ala al-Bakri: 1/107]
Imaam Ibn Abdul Haadi also considers this hadeeth on saying
salaam from nearby according to many Scholars. [As-Saarim al-Munki: 1/115]
Allaamah Shanqeeti writes: “All [Scholars] are agreed upon that this [Prophet’s returning of Salaam]
is only achieved by one who says salaam to him from close….” [Adhwaa ul-Bayaan: 8/838]
Abu Tayyib Shams ul-Haqq al-Adheemaabaadee (rahimahullah) writes: “The correct opinion is that this hadeeth is concerning
the one who visits the [grave of the] Prophet (peace be upon him), as for those who are far away, then the angels convey his salaam to him (and Allaah answers this salaam with 10 blessings).” [Awn al-Ma’bood fi Sharh Sunan Abi Dawood: 6/22]
Abul Hassan Ubaydullah bin Muhammad Rehmaani al-Mubaarakpoori (rahimahullah) writes: “The correct opinion is that what is meant from this hadeeth is the salaam that is said
close to the grave of the Prophet (peace be upon him), as is understood by many other Scholars.” [Mir’aat ul-Mafateeh Sharh Mishkaat ul-Masabeeh: 3/263]
When this much is understood then it should also be kept in mind that Salaam Tahiyyah used to be said during the life of the Prophet (peace be upon him) and he (peace be upon him) used to answer it; and it is also said today so its answer is also given by the Prophet (peace be upon him) himself, as is proven from the hadeeth.
This is also made clear
that just like Salaam Tahiyyah used to be said from close during the life of the Prophet (peace be upon him), similarly, it would be said to him today also from close. You have already read the action of Ibn Umar (radiallah anhu) that whenever he would come from a Journey, he would say this salaam in the apartment of Aa’ishah from close to the grave.
On the contrary, Salaam Ma’moor was used to be said by all the Sahaabah in the prayer wherever they were, so why was there a need to come close to the grave upon returning from the journey? If He (peace be upon him)
answered this salaam even from the person far away, then why would Sayyidunah Ibn Umar (radiallah anhu) come close to the grave of the Prophet (peace be upon him)??
There are two types of Salaam. One is a
salaam that is said from the near which is Salaam Tahiyyah, and whose answer is given by the Prophet (peace be upon him) himself; while the
other salaam is that which is said from far away, the answer to which is not given by the Prophet (peace be upon him) himself, rather Allaah sends blessings on that person instead.
Imaam Ibn Abdul Haadi explains both these types in the following words:
والمقصود هنا أن نعرف ما كان عليه السلف من الفرق بين ما أمر الله به من الصلاة والسلام عليه وبين سلام التحية الموجب للرد الذي يشترك فيه كل مؤمن حي وميت ويرد فيه على الكافر....
“The purpose here is that we know the difference between the salaat and salaam ordained by Allaah, and the salaam of Tahiyyah, the answer to which is obligatory, and in this all living and deceased Muslims are alike, and in which we are to answer the salaam of even a Kaafir…”
[Saarim al-Munki: 1/125]
He further said:
وهذا السلام لا يقتضي رداً من المسلم عليه، بل هو بمنزلة دعاء المؤمن للمؤمنين واستغفاره لهم، فيه الأجر والثواب من الله، ليس على المدعو لهم مثل ذلك الدعاء، بخلاف سلام التحية، فإنه مشروع بالنص والإجماع في حق كل مسلم. وعلى المسلم عليه أن يرد السلام ولو كان المسلم عليه كافراً، فإن هذا من العدل الواجب،ولهذا كان النبي صلى الله عليه وسلم يرد على اليهود إذا سلموا بقول ((وعليكم))
“This salaam (salaam Ma’moor) does not demand an answer for the one who said it, rather it is a Du’aa & Istighfaar of a Mu’min for other Mu’mineen, there is reward of Allaah in it. The one for whom this Du’aa is made, it is not necessary for him to return a du’aa similar to it; as compared to Salaam Tahiyyah for verily it is ordained upon every Muslim from the Nass [of Qur’aan-o-Sunnah] and the Ijmaa of Ummah, it is from the right of every Muslim. And for whom Salaam Tahiyyah is said, it is obligatory for him to reply it, even if he [the one who said the salaam] is a Kaafir. This is why when the Jews would salute the Prophet (peace be upon him), he would reply them with ((Alaikum))”
[Saarim al-Munki: 1/118-119]