There's alot we don't know about this because it's not in the article.
We don't know if they were on the desk or in it.
We don't know if the lid was on or off.
We don't know if it was an isolated incident or if she'd had things taken before.
We don't know if he denied it outright at first (because he's a liar) and only changed the story when confronted with CCTV evidence.
So admittedly based largely on guesswork, this is how I see it.
I don't think he thought they were communal. I think he just thought - ooh look someone's got biscuits, I'll have some of them - what can they do - sack me?
She's come in, been quite rightly annoyed, and asked the company to investigate.
From that point on it's down to them isn't it? It won't be her demanding that he get the sack, and presumably she wouldn't have known who the culprit was - it could have been another woman, so Git's accusations of anti-male sexism are nonsense.
The lesson here is, if you want to keep your job, don't be a thieving git.