By "hindering the development of a YouTube app" you actually mean requiring Microsoft to obey the terms of service, right? The sort of co-operation Page was talking about doesn't mean Microsoft can do whatever they want, demand whatever they want, and everyone gives it to them on a plate for nothing. It means cooperating to find a reasonable solution that works for everyone. In this case, there's already an HTML5 website Windows Phone users can access, and if WP becomes popular enough then probably Google would make a native app that follows content creators requirements and allows the site to be funded. Or maybe provide the access they need to build a proper app that does follow the ToS. After all, that's what happened with the iPhone app despite the iPhone being Android's biggest competitor (it started out written by Apple and later moved to being written by Google).
This is sickening. If your views are representative of how everyone in Google thinks about the fiasco (I honestly hope not), the kool-aid you're drinking must be wonderful.
Perhaps "cooperation" in Google really means "just play by my rules but we won't help you unless there's profit to be made", but it's not how the world is understood by the normal person. Make no mistake, I do think Microsoft is being a dick when they decided to intentionally ignore Youtube terms and conditions when making their own app, but I don't think this vindicates the behavior of Google trying to block them from making a native app. Besides, if Microsoft is doing this as a calculated move to force Google back to the negotiation table for youtube API access, then that says a lot about Google's commitment to practice what they preach about "cooperation".
"Cooperation" doesn't mean "we'll help you if the venture becomes so profitable that we just can't ignore you", just as "cooperation" doesn't mean "we'll comply with your terms after you send us C&D letters". "Cooperation" doesn't mean "be nice to us, maybe one day we'll do a favor for you (no guarantees!)".
To be clear, I don't think there's a moral duty for Google to provide competitor's platforms with the best experience (if HTML5 was so great, why would Google bother to write a native app?) when using Google's services, after all, it's a dog eat dog world out there. However, the "cooperation", "play nice" message by your Great Infallible CEO is sickenly hypocritical at best. Hint: when you make the world a better place, you make the first step. You don't point fingers at everyone else demanding they comply with your grand visions and blaming them when it doesn't work out.
It's also funny how you lambast Microsoft over aggressive license fees, then in the same post justify how complying with Youtube's terms and licenses (c.f. "funded") is so important. I mean, proprietary is bad when you can't use it, right?
Disclaimer: I don't work for Microsoft.