Broham is sounding more and more like a tool. Hate to say it. I need to look at those other regs you cited, but unless they reinforce/further identify specs for shipping containers, the guy doesn't have a leg to stand on.
Observe; part 1. A rubber band securely seals a plastic bag. aka primary receptacle.
Part 2, a bunch of paper towels or other such inexpensive packing material will suffice. I believe home stores sell absorbent material, and even kitty litter/puke absorber would work. If you're shipping flat rate, then costs can be managed. I like to put a disposable aluminum foil tray in the bottom of the box; if the PO is doing its job and handling live animals with care, the tray stays on the bottom and collects water in the unlikely event of a bag breaking.
Part 3,this is his strongest argument, and it's fairly weak. True, the waterproof part might be a little tricky, but not necessarily. Might have think outside the priority box on this, but hit up a catalog/website like U Line. https://www.uline.com/Cls_shipping
Probably something there; you can't be the only person to ever have to ship liquids. You don't have to use a priority box to ship priority. And observe, there is no 70 lb crush rating in what you have posted.
It is possible that the additional stuff they quoted may beef up his case. I'll check into them later.
At this point though, I suspect you're mud-wrastlin' a pig. You're both gonna get dirty, but the pig likes it. Let him have his shallow victory, ship at a different PO, and have some peace. Now if the other POs start singing the same tune, it's time to get fighting again.