Thanks to dfchang813 for the detailed explanation of how this works.
Throughout my guide, I use the 'exploit' where I give my teammate a powerful weapon (like a Boomshot or Torque Bow), because I believed they have infinite ammo with these power weapons. This is NOT TRUE. Towards the end of my guide, I noticed that my teammates would switch to a pistol and never switch back to their power weapons.
The easy (and short) solution to this problem is to give your teammates ONE power weapon, and one weapon that has LOTS of ammo (like the Lancer).
The detailed explanation for why your teammates get stuck with their pistols out:
You have a Boomshot with 5 shots and you give it to Baird for instance. You give it to him as a PRIMARY weapon. His secondary will be something like a Shotgun or Longshot, etc. Well, during a long drawn out fight (that happens frequently on Insane especially as we progress through the game) he will immediately run through his Boomshot ammo. In-game you can actually hear him say "I'm out" or "I need ammo." What does he do? He puts away the Boomshot and switches to his secondary weapons. But remember that since you took away his Lancer or Hammershot or whatever rifle he had as a primary, his secondary gun has very few bullets too Maybe 8 to 10 bullets for a Longshot or 18 Shotgun shells? What happens if you get unlucky and he uses up all the ammo for his secondary? Obviously all that's left is the pistol and he will then pull that out.
As you clear areas of enemies and hear that "gong" and then proceed through checkpoints, the ammo WILL REFILL but if a LONG, LONG firefight forces them to use up ALL their ammo on both the primary and secondary guns, then they are stuck with the pistol and so are you.
So how to rectifiy the problem? EASY. Simply exchange the weapons of your choice and give it to them as their SECONDARY gun. You press A instead of X to switch. Believe it or not, the AI is smart enough to immediately switch out the power weapons into hand even though you did a "secondary" gun switch. In other words if they have a Lancer and you change their shotgun with a Boomshot, guess what? They immediately switch the Boomshot in and put their Lancer away.
The beautiful thing about this of course is that once they use up the Boomshot, they'll put it away and out comes the Lancer with its 240 ammo. And you will NEVER run dry on those.
A checkpoint later, they all have refilled Boomshot ammo again for the next run.