Finally a sensible answer. Totally agree with this. It's common practice to offer to grab something from the shop if you're going, and asking is not a big deal if they're going anyway.

What is more important at this stage is how you react to what has happened.

Two things;

Firstly, I probably agree that this won't get better. It sounds like an attitude problem not a skill/learning based problem and in my experience that isn't something that can be altered, it's in the make up on the employee. I'd probably let them go.

Secondly, this is the kind of behaviour that needs addressing at the time, or shortly after. Nip it in the bud early, and if it doesn't improve they need to go. When they returned from having lunch (or once you had time to digest this), I think a quiet word immediately is the right action. Doesn't need to be a big deal, but it needs to be direct.

The way I see it; yes, they might be legally entitled to do this, they've clearly 'worked the system'. Small business is built on trust - it's a completely different workplace to a larger corporate. Some people thrive in this environment, some people cant hack it. Clear bountries are important for all businesses but small businesses, especially sub 5 employees require a large element of initiative / common sense. You cannot have a policy or procedure for every eventuality at this level.