You are entirely missing the point.The fedral funding goes to the states and they distribute it. Federal funding only accounts for only a small portion of the actual funding that goes to the schools. Its mostly state money thru taxes and whatnot that fund schools plus local govt money and sometimes thru private funds that donate.
I don't care if a school only wants 1% of its budget to be federal. If a school wants federal funding at all, she needs to step up and say that they cannot discriminate against any student. It's actually about 10% at the moment and continues to go up rapidly, but that's beside the point and a debate for another day (on whether or not the US should spend more federal dollars on education).
She's the Sec of Ed. Why would she want to allow discrimination against any student seeking an education?