Google would like to keep the APIs to itself because it can use the better YouTube/Maps/Whatever experience to sell more Android phones and harvest more personal information for their marketing partners. They have no reason to hand over any part of their service that will make Windows Phone better.
The reason they allow Apple access to the APIs is simple: although Android has a far greater market share in terms of phones sold, iOS accounts for nearly 74% of the profits generated in the mobile market. The fact is, iOS users are more valuable to Google's marketing partners, which is why the company did such a rapid about face on their mapping app (remember they didn't want to give Apple access to turn-by-turn or voice commands) when Apple released their own mapping application. Google is even bragging that their iOS version of Google Maps is better than their Android version.
MS is in a tricky position; their small marketshare in the mobile space means they have no leverage. But they do have one big bargaining chip: the patents they're using to extract money from the Android OEMs.