Lungs burst due to expanding air?

In "The Shark Cage," a supposedly trained and experienced diver gives his tank to a man trapped in a shark cage whose air has run out. He takes a breath and then frantically swims for the surface. Mike Nelson's narration says that the guy was too deep to make it to the surface on just one breath.

Totally wrong. At least, it is now. Wasn't it known by 1958 that you did a slow ascent while continually exhaling? The air in the lungs was breathed in under high pressure. As the diver rises, the pressure decreases. If the diver tries to "hold" his breath, all that air that was breathed in at 100 feet is going to expand and burst the lungs. If the diver continually exhales while rising, the excess pressure is released. So, no matter how deep, there is always enough air to get to the surface.

Somewhere in the past I read that there were probably a lot of submariners who died in their sunken boats because it was thought that they could only escape if the sub was at 300 feet or less. Again, once the escape chamber was flooded, the air being breathed is highly compressed. Take a deep breath and exit. Rise slowly, exhaling continually, until you get to the surface.

Now, I don't know how deep a person can go and the compressed air will compensate for the increased water pressure. I'm sure there is a limit. Also, I know that a normal sea level oxygen/nitrogen air mix becomes deadly under pressure. So, there must be a limit to how deep a sunken sub can be and the crew can still safely exit via the escape trunk.