The instant you finish the connection, your alternator senses the new load and wants to put out a full charge. But if you're doing the jump with your car just idling, your alternator isn't turning fast enough to put out all it can. So, it heats up. And yes, you can end up burning out YOUR alternator by jumping someone else's car.
I can see this happen if the voltage regulator is malfunctioning, but I have used my little Civic to jump start large pick-up trucks. When my Civic alternator senses the new load, it doesn't overload itself. It simply takes more time to charge the big battery. Sometimes it takes five or ten minutes before the truck can start, and sometimes it will only start if I hold the throttle on the Civic, but after 187,000 miles, 11 years, and several jump starts of larger vehicles, I am still using my original alternator.
In order for your theory to hold, something on the running vehicle (maybe the voltage regulator, maybe the alternator itself), must be malfunctioning or on its last leg. If this theory held true, my alternator would die every time my battery dies. It doesn't.
I think cases like this where someone suspects a jump start damaged their alternator happen because the alternator was on it's last leg anyway, and doing the jump start pushed it over the edge a little sooner than would have happened otherwise.
Oldschool, I don't think stachi is an ASE master tech. I think stachi is quoting a response from another forum.