I've noticted the Marines use a 20" Hbar version of the M16. I've also heard "shooters" at the range who won't fire more than 1 round each 5 seconds so they don't harm the match barrel.

So what is the real deal?

Combat rifle barrel and match barrel are two different animals.  Hbar's are thicker so the dissipate the heat better.  Full auto for awhile could probably harm the barrel, but not unless you dump a few hundred rounds down it extremely fast. (so I've heard)  

FYI,  I don't think my M4 barrel is harmed, and I've dumped a few hundred down it within a minute or two.  

There are two different reasons here. And neither of them involve doing perminant damage to the gun.

Match shooters use slow fire because they don't want to hurt their groop size, not damage their barrel. They are waiting for the tempertaure and also the vibration from the previous shot to return to the same level as the previous shot. So all shots are as consistant as possible.

The Marines don't use HBARs. They prefer the A2- and have said they won't go to the M4- because they want the velocity, primarily for the wounding effects, to a lesser extent for the longer engagement range. But they are still A2 profile barrels, which are only thick infront of the handguards and for a short streach in front of the receiver, over the chamber.

The most noticable effect of this for the shooter is that the extra metal acts as a heat sink and increases the time you can fire full auto without the rounds cooking off in the chamber.
  For the military, it means that the barrel can stay in service longer before it becomes too warped from the repeated heating-cooling cycles to meet the 4moa minimum accuracy requirement for a rifle barrel to be declared worn out and due for replacement. That means they spend less money servicing the fleet.

During the Vietnam era the military had become somewhat concerned by the rate at which the M16 fleet as a whole wore out barrels. Guns were being rebarreled that were only a couple years old whereas large chuncks of the M-14 fleet still had their original barrels. Examination revealed that a substantial number of the chrome-lined A1 barrels that were failing to pass muster still had very serviceable rifling. The problem was traced to the heat build up from firing on full auto ALL the time, made worse by abuse (people falling on them, using the barrel as a crowbar, ect) causing the barrels to get bent.

Its not possible for a civilian shooting a semi auto AR, even one with the old "pencil barrel" to get his gun hot enough to cook off rounds, or to put it through so many heating cycles as to warp it. Even in the military, since the change in barrel design was ALSO accompanied by the introduction of the 3rd burst feature, that combination makes it difficult to damage the barrel now.

Uh, not exactly.

Rapid fire, and especially full-auto fire, will erode a barrel much faster than once-a-minute fire.  Ask any benchrest shooter.  The standard is to wait about a minute between shots.  Yes, it helps keep things consistent among shots, but it also helps keep those expensive barrels good for more rounds.

Meanwhile, run a barrel until it gets red hot, as some full-auto folks do for fun, and you've basically got a bullet hose.  Yeah, it's a kick, but you aren't going to be shooting sub-0.100" groups out of it any more.

Five seconds in between, well, it's better than nothing.

For something with as crappy an accuracy potential as a basic AR-15 rifle, HBAR or not, it probably won't make much of a difference.  If you've got a Krieger (or other match-quality) barrel on your spacegun, though, you'll want to take care of it.