Is the grammar correct again?

I think Sturm is asking a two part question:
1. How are institutions of higher learning trying to minimize their legal exposure, and,
2. Are they doing so at the cost of diversification in their student bodies?

Lazy (hurried?) writing. My rewrite should show one way to handle quoted questions:

The grammar looks "wrong" because this is reported speech which does not always conform to neat rules. If Sturm were writing about the issue herself she would be obliged to put something like : "there is the question of how they are doing that, and whether they are doing it in a way.............body".

It's a liitle bit loose, but remember it's reported speech. We don't always speak in excellent grammar- sometimes for sound reasons, e.g. brevity.

I would say "... how are they doing that...." is an actual question.

"...how they are doing that..." is not a question, in itself.

I think the original is okay, in the register and context in which it was being used.

No, this is NOT reported speech, nor is it lazy hurried writing.

Reported speech does not use quotation marks because reported speech is not a direct quotation, which this obviously is. When someone is quoted directly, there is no change made to anything that the original speaker says; hence direct quotation.

There is nothing grammatically wrong with what the law professor said. The normal neutral is to not have a grammatical question form in a statement. We are not compelled to always follow that normal neutral. There are situations, like this one, where the speaker may wish to make it more emphatic, sort of a,

The question is -- how are they doing that ...