Isn't that what the article is saying? Less research funding == Fewer admissions.

> The number of graduate student admissions is directly tied to the amount of external funding.

Minor quibble: It's not merely external funding. In many sciences (math, physics, chemistry), it's common for the department to promise funding through non-research means for a number of years. In my top school, I think physics students were guaranteed TA funding for 2 years (until they pass the qualifying exams and find a professor). Math students are almost always funded as TAs (the department guaranteed 6 years).

It's mostly engineering departments that don't do this.