This question is based on a false premise: That the congregation says Tachanun because the Aveil is present.
if an aveil (mourner) is present in shul during his week of shiva, the congregation does say Tachanun but the aveil doesn't.
It's the opposite: If an Aveil davens at home in a Minyan, the entire Minyan doesn't say Tachanun, because he can't. Since it is his home (usually, or it's his current abode) they have to follow him.
But, in shul, he doesn't have the "power" to prevent others from saying Tachanun, so they ignore his presence.
A Chattan and Mohel, on the other hand, do have the "power" to prevent others from saying Tachanun. Probably because everybody wants to join in the Simcha.
I guess nobody asked the Aveil to come to shul and they have no intention of joining in his mourning. (Actually, he's not even allowed to come to shul unless he can't gather a Minyan at home.)