This is correct; scuba divers are trained to do a controlled emergency ascent while continuously exhaling, because your lungful of air at depth will last the whole way up, and the real risk is not running out of air, but embolism from overexpansion.
The limiting factor in ascent (and therefore the reason for the recreational dive limit of 60 feet) is the risk of decompression sickness. If it weren't for that, a diver at arbitrary depth could ascend on a single breath.
This is not entirely true, not all agencies teach a Controlled Emergency Swimming Ascent (CESA). From memory the only one that teaches this is PADI.
Most don't as this is not a very effective or safe way of getting up once you get bellow a few M of water.
Most agency's will teach you to do an Alternate Source assent where you come up breathing of your buddy's air source, as this allows you to come up at a safer and more controlled rate.
As I remember the PADI training the CESA is the absolute last resort when your buddy is not available. I imagine all authorities would agree that it's less bad than remaining at depth without gas.
No novice diver is going to remain at depth in an out-of-air situation, under any circumstances. The point of training the CESA is to teach people not to hold their breath and hurt themselves when they panic and bolt for the surface. This panic reflex is so strong that it takes dozens of hours of training and practice to be able to signal a buddy and breathe off their air supply in a real emergency situation.
You can see this reality reflected in the rescue diver certification (a fairly advanced level of training), which revolves around how to stop people bolting for the surface when they have trouble getting air. Rescue divers are taught some fairly extreme measures—you pull the person's regulator, yank their fins off, pull off their mask, and hold them down by the tank valve, anything you can do to prevent them surfacing at high speed. Better a briefly unconscious diver than one with an air embolism.
The beginning certification level is 60 feet. You unlock the deeper limit after additional training, and it includes performing a three-minute "safety stop" at 5 meters. 60 feet is about as deep as you want to shoot to the surface from (and if memory serves the limit they give in training is 30 feet, or 2 atmospheres).
I've always been fascinated by how hard diving is. 60 ft seems like a completely trivial depth - about the length of four cars - but already there are non-trivial risks. And from there it rapidly becomes more dangerous and complicated and just plain hard to stay alive.
The limiting factor in ascent (and therefore the reason for the recreational dive limit of 60 feet) is the risk of decompression sickness. If it weren't for that, a diver at arbitrary depth could ascend on a single breath.