From the letter of the Mahril that, in Haditch by the gravesite of the Alter Rebbe, there was a wall

This was done so that Kohanim could go there. The rumor that you heard needs to be verified, but there is a difference between the funeral and going to the gravesite later on. https://www.torahrecordings.com/rebbe/igroskodesh/011/010/3608