Lawyers and doctors aren't undergrads.

Medical research depends heavily on faculty and postgraduate folks.

Only some of their thousands of annual graduates are undergrads - about 1/3 of them, per Wiki.

I am confused. Who says credentials only apply to undergrads?

I said they do more than teach undergrads, to which you re-quoted me questioningly.

Include postgraduate folks and they're still doing a lot more than just teaching and credentialing. Places like Harvard output research, too.

A university research lab is controlled by usually one professor or a very small number of professors. They can decide to move to another university and take the lab with them.