[RealJames]

I dunno, I've heard pretty differing stories that lead me to think that it comes down to the immigrations officer dealing with it.
In my case it certainly was that way, one immigrations officer flat out denied my business visa, so I went to the office another day when he wasn't working and his coworker felt I was overqualified for it and accepted it on the spot right there.
It might help to mention I was sleepy and dressed very casually the first time but in a suit the second time.

If a company wants you there's nothing they can do if immigration decides you don't meet some obscure criteria.
If immigrations likes you for whatever reason then you'll have no problems staying in the country even with a part time job and crap salary below official requirements.

From experience, I was working part time at a crap English school making very little money on paper, supplementing my cost of living with a slew of private students. But on paper I was making about 12万円 a month. I kept trying with different officers until I found one that liked me and then got in no problems.

Over-stayers is a different problem, that's just stupidity and also disrespectful.
I meant lax in terms of who they let in.