I think Facebook should cozy up to Mozilla and use Boot2Gecko. Facebook's strength is in their web presence, and by leveraging a web-oriented phone, they could offer something that doesn't compete directly with other handset makers.
Mozilla would curl up, sell/give their assets to charity and die before partnering with Facebook. Boot to Gecko is free, open source, and arguably more "open" than Android. There's no need for a partnership. Mozilla and their leadership care very much about privacy and freedom. Facebook does not jive with that at all.
Furthermore, facebook might be somewhat evil when it comes to customer data, but they're an upstanding citizen in the open source community. they manage or contribute to many open source projects.