Who said anything about trust?
I mean sure, Murph's liable to "trust" a non-infected human dude with a sword a bit more than he's gonna "trust" a screamin', neck-gnawin' zombie but "accepting Brian into the group without much debate" doesn't have anything to do with "trust"...
It's a matter of numbers, really... Another body in the party gives us better odds of lasting longer, after all... Besides, what's to trust? It's not as if we've got a whole great deal that anyone's gonna take from us, right?
Heck! We don't even have a place to sleep yet.... just a meager stock of groceries, some medical supplies, weapons, dwindling ammo, and neuroses is about all we've got... and who's gonna take that from us? Zombies most likely!