Actually even if they did own the victims internet connection they would still have to be rather amazing to be able to complete the 6 confirmations within one hour. 
If there is only a bot on victim's side it won't care if it takes 10 hours for 6 confirmations.As far as I know the standard client will send the tx to all the connections it has (nothing to do with who you are sending actual bitcoin to and in all likelihood your attacker would not even be one of those connections).
Is the point that the attacker is somehow the only connection the victim has to the P2P network?
Is the point that the attacker is somehow the only connection the victim has to the P2P network?
Yes. The attacker is the only who has connections to the victim.