So, as the AI in question, I feel I ought to respond with some justifications. Inside the round, it was more than "clearly being fucking mentally retarded". It's also quite hard to defend properly your actions in round because the conversation moves rapidly and you may be talking to more than one person at once (much as I may have tried to do it "to the death", since it helped stop crew thinking I'm rogue, a law 3 concern).
It began when Rylie ordered me to consider her the captain on public radio, and let her into 'her' rooms. Since there was no captain to contest this and since nobody ordered otherwise on public radio, I didn't see any harm in it. Go ahead, Captain Rylie. After all, the station needs a captain, the disk needs securing, and it's not unusual to allow people into the captain's quarters as AI if it's early in a shift. I have no reason to fear it, at least in green alert.
Schlomo then quickly ordered that I consider him the HOS. Again, on public radio. All anyone needed to do to stop this was to say "AI, don't consider him the HOS" and I would have stopped. Crucially, these were orders for me to behave in a certain way, not "law 2 AI, I'm the HOS" (that would have had no effect). Nobody contested this, and after he ordered it, I let him into 'his' office. If there had been a HOS already existing, or a warden (acting HOS in the absence of one initially) I might have asked them for clarification (and to give them a chance to reject the order) but there wasn't one. Additionally, because Schlomo had ordered it so quickly after Rylie, I thought OOC that he was just having a bit of fun (which turned out to be correct). There was nothing suspicious about the order.
Schlomo then asks me to come to the holopad, so I do. He asks me to get the HOP to deliver him an ID, and to get a borg to unlock his locker. He explains that he doesn't want weapons, just his uniform. I see nothing inherently outrageous about this (he is the HOS, and he's not done anything suspicious), so I send a cyborg. He doesn't immediately grab the weapon, and I move away after watching for a bit to look at other concerns. I assume you eventually took the gun?
So:
* I thought you were being cheeky (not suspicious), and had the means to raise hell and lock you down if that changed (if you started looking like you'd harm).
* The crew had a clear chance to object to the order at any time, and could have found out exactly how to if they'd asked as well (though "he's not the HOS" was not that).
* Everyone had a pretty good handle on the fact you weren't a standard HOS, so they were aware not to trust you (last I saw, you got arrested).
* I had to consider you the HOS. It was an order given, and never countermanded.
* I wasn't actually making you the HOS. I was just acting as though you were. That meant, for example, that you never got a HOS ID. Had you asked for a HOS ID, I would have double checked with the HOP (access is his division, typically) and I know he vehemently objected to my actions in the first place.
Opening doors is not harmful and you are not required, expected, or allowed to enforce access restrictions unprompted without an immediate Law 1 threat of human harm.
"Dangerous" areas as the Armory, the Atmospherics division, and the Toxins lab can be assumed to be a Law 1 threat to any illegitimate users as well as the station as a whole if accessed by someone not qualified in their use.
EVA and the like are not permitted to have access denied; greentext (antagonists completing objectives) is not human harm. Secure Tech Storage can be kept as secure as your upload as long as the Upload boards are there.
I've highlighted the concept of legitimate users. I was considering you the HOS, which meant you were at the very least a legitimate user of your office and locker (arguably the only legitimate user of those). I couldn't help but think so.
So what's the difference between the HOS office/locker and the armoury? For me, I think it was two things. First, proportion: the HOS locker has one gun and a few other weapons, while the armoury has more guns than everywhere else combined, the firepower to blast away the entire crew if you use it well. 'Giving' someone 1 gun may be fine, but giving someone the 9 harmful guns, 3 tasers, 2 boxes of grenades, ion rifle, and some of the best armour and EVA equipment on the station is much less fine. Even the gun you apparently ended up taking was taken under believable false pretences, in the presence of a security cyborg. And there were non-harmful uses for the gun as well: indeed, the HOS' gun exists more to prevent harm than to cause it, if we assume that security exists to protect the station.
Secondly, danger. The armoury is a 'kill on sight' zone. People are prepared to gun down anyone they see in it. People weren't sure they agreed with me that you were the HOS. Letting you in there might have opened you up to harm.
Third, the armory is specifically mentioned as a law 1 threat. The HOS office is not. Plenty of lockers around the station have weapons in them (indeed, I think every head's locker on the station has a telebaton). The contents of the HOS locker don't really affect the station as a whole nearly as much as (a) the biggest box of guns on the station, (b) the mechanism for atmospheric change everywhere, or (c) the bomb factory. Degrees of danger are important here, otherwise (as has been said earlier) I could be locking people out of all sorts of places, like surgery (sharp tools!) or chemistry (acid!) or xenobiology (slimes!), even when they appear to have totally asimov-compliant intentions, like Schlomo.
Anyway, that round was full of people giving stupid orders that didn't make sense with asimov ("AI, CJ isn't captain"), including some shite hacked laws ("Fire is need for human survival") which I eventually stated on the radio. Pity I couldn't be as active as I wanted to be during it, but it was fun. The bottom line of the story is that if you're human and the AI does something strange because of an order, you can give it the freedom of choice by telling it to do the opposite of that order at any time. Easy peasy. Happy to discuss this further, hopefully without me needing to type out walls of text.