Or they just ignore somebody shooting him for no reason also YAY!
Seriously sometimes I wonder if some people watched a different movie than I did.
They didn't know he had been shot. I'm wondering what movie you've been watching? They didn't know he had been shot until they had recovered him and brought him aboard the Enterprise
for inspection and repair.
If the sector wasn't contested, the Federation likely would've had little to nothing in the way of a presence there. The S'ona could've came in and simply beamed the Ba'ku up or cooked them from orbit with the Collector with the Federation/Starfleet being none the wiser.