I didn't realize Fateev was taking the graduating students from schools that are the equivalent of the University of Kentucky and offering them Soloist positions in the Mariinsky.
If I followed the news stories correctly, there was an attempt to have the Academy come under the auspices of the Theatre, allegedly (as posited by official sources) to take over the Academy's studios for the Mariinsky while the old theater is renovated, and it failed. The Theatre doesn't control the Academy, and the Academy can continue to produce dancers according to its own standards. It can't, at least at this point, force the Mariinsky Ballet to compete for or to use the Academy's graduates or to prevent them from hiring from the outside.
The Mariinsky is a company that is funded by governments, corporate sponsors, and private individuals, some as a result Gergiev's personal efforts. Gergiev was appointed the head of the Mariinsky Theatre. Whoever appointed him can remove him, if they feel his policies or his hires are ruining a national legacy. Governments can pull funding if they don't like what he or his hire is doing. Either they agree with his policy, or haven't been convinced to take action against him.