While you might claim that running an ASOP derivative you need to trust Google less (and in turn trust something like f-droid more, perhaps) -- if you want a chat/im client on an Android device it's hard to see how Google isn't already one entity you need to trust (along with a list of hardware manufacturers).

As for your other comments - you may run your own server infrastructure from same or derived sourced, your own derived clients, distribute binaries etc - but you can't dilute the brand. Similar with Debian cloud images for example.

I'm not sure how that's "not FOSS".