You have come across what is known as the XY Problem. The real problem is not whether you should be "allowed" to use backquotes in comments. It has been repeatedly emphasised on the SE network that "comments are not for extended discussion this conversation has been moved to chat " but to improve the post on which you are commenting.
If you are about to comment something which requires quoting another user, you are, in most cases, not using comments for the intended purpose. Comments should only be addressed to the user whose post you are commenting on. In those cases, quoting the user using quotation marks is sufficient.
Getting into a discussion with a third person is not at all the intended purpose of the comments. If you and a third person disagree on how the poster should "improve" his post, that should be taken to chat.
My misadventure experiments under enderland's answer made me realize that (some) HTML tags are not allowed in the comments because they just didn't care comments are not meant for meta-humour either.
Disclaimer: I am not preaching from a moral high ground here, as I "amuse" myself (and others) a fair amount here in the comments.
By the way, it is fair enough if some formatting tags are not useful on some SE sites. For instance,
spoiler tag is useful to Anime.SE, Puzzling.SE, Movies.SE, etc. but not here.
and
$ whatever they call this thing is useful to Mathematics.SE, MathOverflow.SE, etc. but not here. $