I think much depends on one's perspective.
If you view the world through a prism of rage, then, it is entirely possible that any response short of obsequious servility will be taken as a source of possible offence.
I have to say that I have never thought that any post which read "works for me" was snarky in the least: Rather, it was merely notifying those reading that this problem didn't apply to them, which may serve as useful information to others when mapping a particular problem.
Agree, although "works for me" could read as snarky or rude if one has recently read a bunch of other threads where seemingly valid concerns or complaints were met with some one-liner "works for me" dismissals.
I'd probably not say exactly "works for me" in a genuine reply to a tech issue though. That is precisely because I do sometimes use that phrase as snark in real conversations with friends... but generally not online, or at least not without some indicator that I meant it sarcastically.
If I do mean to reply that I don't have a problem someone else has reported, I usually just say something like "I haven't experienced that" or "I ran the update and so far no problems" and supply info like device model etc.
I tend now to check myself when tempted to say "works for me" with intent to discount someone else's report of problems. I suppose I am suspicious that some of the complaints are spurious and put up by competitors, but realize that might be unfair depending on the issue, since any manufacturer can encounter production problems.
There was a time when after buying new Apple gear I'd avidly follow threads about user experiences, but I don't much do it any more and it is because a lot of the discussion seems quite negative while I'm still excited with my new purchase. Of course there can be more real problems now as manufacturing volume increases and so does pressure to meet tough deadlines, right along with complexity of assembly, but it's hard to get myself to sign up for reading a grouch thread when I'm enjoying the device or the upgrade...
I did like the new hardware threads better when more people seemed "lucky like me" and were reporting user satisfaction. Sigh.... even given that most people do log into tech sites to seek help or report problems, not to heap on praise, my retreating reaction might not be uncommon. That could mean that competitors' "downvoting" tactics are working in a PR sense, no matter if the rest of us when we do post resort to sincere "works for me" comments, or to lengthier defenses of new Apple gear that we're enjoying.