This is for two reasons:
1. Suppresses duplicates correctly, as the notifier doesn't do any
duplicate suppression.
2. Makes it easier to connect the AppserviceHandler to the replication
stream.
Access it directly from the homeserver itself. It already wasn't
inheriting from BaseHandler storing it on the Handlers object was
already somewhat dubious.
Bug introduced in 92b20713d7
which reversed the comparison when checking if a user existed
in the users table. Added UTs to prevent this happening again.