Pig is thin alright, but I regularly use the Tandy stuff as liner inside bags I make. So far they've been camera bags, but it works so well and looks so cool I may try some soon in a possibles bag. Stiffens a soft leather up just right, so if you're working with deer, elk or Tandy's Deertand cowhide, I bet the bag comes out just right.
That makes me think you could use that hair-on hide for an outside "liner." Just do like I do- glue it to the leather pieces before assembling the bag. I've used Barge rubber cement for years, but the toluene in it will sure lift your spirits if you use it indoors.
Lately I've switched to Tandy's EcoFlo water soluble contact cement. It's latex based, and smells just like latex housepaint. But man, is it ever good stuff. Hard to imagine, but it appears to work even better than Barge.