We've for a long time had the behavior that a bot mentioned in a
stream message receives the notification, regardless of whether the
bot was actually subscribed to the stream.
Apparently, this behavior also triggered if you mentioned a bot in a
private message (i.e. the bot would be delievered the private message
and would probably respond unhelpfully in a new group private message
thread with the PMs original recipients plus the bot).
The fix for this bug is simple: To exclude this feature for private
messages.