Sheppard: (referring the alternate McKay) We put him here in the guest quarters until we can find something more permanent.
McKay: Something more permanent? Well, we're not keeping him!
Sheppard: He can't go back.
This is similar to an incident that happened at Stargate Command in the Stargate SG-1 episode "Point of View." The alternate Carter was experiencing what they call 'Entropic cascade failure'. It happens when someone from another reality shares the same reality as their counterpart. Later, it will involve the death of the alternate person. The alternate McKay would have not been able to survive in their universe since the original McKay of the universe is still alive.