With Signal, you clearly do as they send a lot of your information to Google explicitly (like contacts) and Google has root on your phone.
Is that completely accurate? As Moxie explained elsewhere they do sync contacts, but that's optional. I'm not sure there's any other dependency beyond the GCM push, which I don't know is very concerning.
Google definitely has root on your phone, but is that automatically an implication that Signal is compromised?