This is an example of why federal grants-with-strings must be stopped. By offering to pay, the feds implicitly admit they're too far outside their Constitutional sandbox to simply mandate compliance, which in turn demonstrates that they're controlling funds in excess of the amount necessary to carry out their proper functions. Ergo, they owe us a refund.
Undo the 17th Amendment and I think you'd have relatively little trouble with grants-with-strings. For years now I've been angered by the way my state's legislature dances to those marionette strings.