it seemed like between 7,000 and 8,000 the air is not suitable, but I figured the pilot wasn't likely to be taking risks like that, so there must be some explanation

Yeah, I mean the atmospheric pressure at altitude varies, it's definitely not black and white. And it's true, pressure does start to really drop off around 7000ft, but it's just starting to drop significantly at that point, that just makes 7k a good ceiling.

So yeah, this all seems pretty much consistent.