But understand, that's the GM putting on the hat "small group human resources manager" and it has nothing to do with properly refereeing the game.
With respect, I think this is a profound misunderstanding of the role of the DM. Those two hats are the same hat. You cannot be a proper nor successful referee of any kind without being a "small group human resources manager".
What's interesting to me, I've seen DMs attempt, crudely, to act as neutral referees, but who lacked the basic tact, empathy, decency and so on to act as a "small group human resources manager" (because they were ill-mannered teenage boys lol - I was suave and empathic by teenage boy standards lol), and it always, without fail, created 10x as many problems, debates, and complaints as not trying to be "True Neutral" would have been lol. Especially 90% of "neutral" DMs are biased towards regarding their first instinct as "right" and hard to budge even if the rules clearly say they're wrong.
If this is a tournament, the GM is not only right, if the protest continues you call over the game runner and then probably player either concedes or is removed from the game.
The mistake here is to treat D&D as a game suitable for "tournaments".
It is not.
D&D is essentially a creative game, with flexible rules, a ton of unwritten ideas (most coming from the DM), and trying to play it like it was a computer game might be fun at times, but it's not the "gold standard", nor should general advice to DMs ever be based on "tournament" approaches. That's a truly early 1980s idea.
So in my view that literally couldn't be less relevant.
But I also believe that in practice the most likely situation is that the GM is going to compromise with the unskillful and possibly even antisocial player just to keep everyone happy and the game going forward. That compromise is likely to be advantage on the saving throw or some other small bonus on the throw to placate the player and prevent a temper tantrum from ruining everyone else's fun.
I think the attitude here quite problematic, because it indicates an extremely severe bias for a man who has been claiming to be a "neutral referee".
You are assuming a large number of seriously negative characteristics for the player, who in reality, is quite likely innocent of all of them. My experience is that DMs are absolutely 100% as likely as the player to be guilty of being "unskillful" or particularly "antisocial", so applying those traits
only to the player rather than asserting the issue could be with either is obviously unreasonable.
And "prevent a temper tantrum"? Most of the worst temper tantrums I've seen actually at-table have been from DMs. I guess partly because when I'm DMing I'm extremely good at keeping people calm, but still. I think the DM having a temper tantrum over his poison not working is absolutely as likely to be an issue. I've seen a DM get mad because his trap got foiled before. I feel like if you've observed other DMs, you're bound to have too (but if you're a forever DM, maybe not lol).
The trouble is, I think, that you're assuming the DM is you, and the player is some awful person you're meeting for the first and last time at a tournament. Not the DM is someone else, not that the player is someone you know.
Another issue here, is neurodivergence, anxiety, and so on. A lot of D&D players and DMs have issues in this regard. So I think it's particularly bad to start assigning them negative characteristics in the way you're doing. It's much more likely the guy blurting out that he's wearing gloves is being genuine but has issues than that he is some sort of "cunning rapscallion". You again cannot be a good DM without factoring this in to some degree.
Further, there's the longer-term impact to look at. Your actions impact the game going forwards. If you say:
1) "Okay, you're wearing gloves, in future let's specify that beforehand, okay!"
Then you're creating a situation which is relatively low-stress, and establishes a precedent of being clear about this stuff. That's good for everyone, and it shows the DM is cooperative, but not a pushover.
If instead you say:
2) "Nope, doesn't say gloves on your character sheet!"
Then you're creating a high-stress, high-maintenance situation that doesn't work well with 5E's fundamentally lackadaisical approach to gear. Your game will slow down in future because people will need to carefully examine their gear regularly, and carefully choose every word they say - which again is extremely challenging for a lot of neurodiverse people (again, a large fraction of D&D players). The stress from having to get it exactly right, rather than having a cooperative DM who checks that they've on the same page about actions before assessing what happens.
You can run a game the latter way. A lot of people used to - it's not popular anymore because honestly it's a lot less fun for most people that way (hence the death of the equipment-obsessed game in general). I don't think it's remotely a good idea, nor really "good DMing", though, if I'm honest.