> There are actually universities who _claim_ to have great math (or physics or other science) program, but actually just teach it at "advanced high school" level.

What do you mean by that? And could you give an example?

It's hard to imagine any university teaching science majors at 'advanced high school' level, as I understand it. I could see a US community college or almost any university teaching intro courses that way. I can't iamgine what a 4th year chemistry major would be studying that fits the scope of 'advanced high school'.