Does HR really look at the university you graduated from?

At the start surely, but for the next stage you still need to rely on your interview skills to stand out.

If you're the HR, based off just 2 resumes with exact same furnish other than an exception; one of it from local u and the other, private. Which will you pick?

Of course they do. The first part of screening is your results and your background

If this sounds interesting to you, if the HR is from local uni, he will tend to favour local uni. And if the HR is from private uni, he will be more open to private uni.

All these are typical human behaviour though people would talk about it openly.

I think so