I also own a Numrich Arms minute man in .45 cal. That has the barrel pins through the bottom of the barrel. I consider it perfectly safe to shoot, and in fact the previous owner shot it with some pretty hefty charges without incident. I have to admit that I did replace the hardware store Allen head set screw they used for a breech plug. Unless it was a lot lighter barrel, or a lot larger caliber, I would not junk a barrel over this. The other thing I have to ponder is why modern builders often slot the pin holes in the tenons, when obviously more than a few old timers saw no problem with a pin sized hole through the bottom of the barrel.
Hungry Horse