Yeah, the symbiote is telepathic, and doesn't actually have to be in contact with someone to begin to control them. It also controls its hosts in their sleep and during blackouts.

Also, in the comic, the Venom Symbiote is considered insane by its own kind and banished, because it actually sort of cares for its hosts. It wants to bond permantly with its host, rather than simply use them and kill them, and the other symbiotes don't want it to spread.

The Church scene is actually right out of the comics, except in the comic, the Symbiote actually drags Peter to safety after he falls unconscious from rejecting the symbiote. In various incarnations, the Venom Symbiote takes any chance it can to try and re-bond with its original host, Peter Parker.

Also, which would have been nifty to see in the movie, is that the Venom Symbiote has much more impressive morphing abilities, and can actually turn into ordinary clothing--and even firearms, if you consider the "What If.." stories as canonical in terms of powers.