In wouldn't say it's about "offending" somebody with something better (or for that matter even necessarily conceding), so much as I don't want to hear somebody with top-tier specs come in here and go off on how I need to check my ego.
I have a coworker who is always one up'ing other people. Say something about a particular hobby, he says he's better. Say something about food, he says it's crap. Say something about a possession (car, electronics, etc.), he says his is better. It gets fucking old, and so every little comment has to come with a disclaimer like "I know [insert name personal possession or skill at something] isn't the best, but..." so he or other people like him don't feel like they got a cue to jump into the conversation and make it about themselves. Probably a futile effort, but it's with the intent to keep those type of people's comments to a minimum.
However, you bring up a valid point that if there's myself, the one upper, and somebody else who is listening who has lesser skill or not as nice possessions, you're right that it may put them off (or offend them).
So you're either trying to mitigate stupid comments from one uppers, or potentially offending somebody else. Unfortunately there's no real winning, but that's pretty much the case with everything in life. It's a zero sum game. Somebody may be winning, but the other person may be "losing" (I put emphasis on that, as it's not necessarily losing, so much as everybody can't be rockstars; having the best of the best stuff or be the best at what they do).
