Re: Johns Hopkins University
I don't think you can make that generalization. Sports fans in the US will be well aware of the emphasis on "the" in The Ohio State University.
You'll often find "the" with the word "university" (in the US).
The University of Pennsylvania, etc.
It seems that Johns Hopkins uses both "Johns Hopkins" and "The Johns Hopkins University" so the "the" generalization applies here.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.