Well then that's horrible. It seems an awful lot like blackmailing to me: "If you want us to keep helping you with your finances, you better find a big name coach, or ELSE." Like what the heck. That's not cool.
Well no, it's not like blackmail at all.
If JSF is really making Hanyu switch coaches in order to receive funding, then it's perfectly within their right to do so (if allowed by the federation's stipulations for funding), since they're GIVING him money. It's only extortion/blackmail if they're threatening to harm him/reveal harmful information unless he complies with their requests, which hardly seems the case here.