My main is a hunter, and I find it interesting that you would have to pull hate off of the hunter's pet. I take this to mean that the hunter was leaving growl on (otherwise, it should only take one of your attacks to get hate back (and was the hunter not sending his pet after the main target? another no-no))- as a general rule, growl should be off in instances, unless the pet *has* to do some off-tanking. Even then, growl technically doesn't have to be on as long as no one else touches the pet's target.
In my all of my groups - PUGs or otherwise - I prefer that the tank take a leadership role. It just seems to make things easier. I think you'll find that as you do more groups, you'll be expected to lead, and as such, make sure any hunters in your groups are leaving growl off and are sending their pets after the main target. Even if the pet gets to the target at the same time you do, or even before, it won't be able to take hate from you if growl is off. Our pet's attacks just aren't strong enough. And yes, the dps should wait to start unloading - not doing so just causes trouble for everyone. The tank has to run around to try to keep the mobs under control, the healer has more targets to use mana on, etc.
Before letting the pet die, I would have sent the hunter a few tells letting him know what he was doing wrong - which you said you did. When you're talking to people to tell them what to do, it helps to know each class at least a little bit, so use what I have told you in the future when you encounter hunters such as this. While our pets have a lot of armor and can take a beating, they don't have near the avoidance or health of a tank, so they cannot stand up to elites for very long. Explain this to them if necessary. It might be you were encountering someone such as myself at that level. I didn't do many instances because I didn't have to (hunters are VERY easy to solo with) and I was always scared that I would ***** up a group hardcore. Hopefully you'll be able to help someone become a better player.
In your case, I would have let the hunter's pet die, and then defended myself by saying that 1) the hunter can control, heal, and revive his own pet - you shouldn't have to babysit it, and 2) you babysitting the pet would hurt the whole group - instead of concentrating on taking down targets quicker, you have to try to keep an expendable group member alive, making everything take longer. I'm of the opinion that if my pet dies in an instance, it's my own stupidity. I have complete control over my pet - I tell it what to attack, when to attack, when to come and stay by me, and I can heal it myself - not as well as an acutal healer, but as long as it isn't tanking, my heals are sufficient to account for AOE attacks and such.
So, in the end, don't worry about what you did. You were right. I have been in some bad PUGs, but if you play well, you'll eventually come across other good players in PUGs who you'll add to your friends list and group with later on, negating the need to group very often with bad players.