This is an hypothesis which astronomers are trying to test by gathering new data. Their work has some immediate repercussions: NASA is currently planning an "Asteroid Redirect Mission (ARM)" as part of America's next human spaceflight enterprise. Understanding the origins of asteroid sizes - and then identifying a good one for an astronaut to recover - are prime US goals.
Comment: This out dated hypothesis is slowly being re-evaluated in light of real cometary science.
"The fundamental difference between asteroids and comets is not their chemical composition, i.e. dirty, fluffy icy comets vs. rocky asteroids. Rather, as has long been put forward by plasma theorists, what differentiates 'comets' from 'asteroids' is their electric activity"
Earth Changes and the Human Cosmic Connection
For some in the mainstream astronomy community the penny is finally dropping: Mars moon Phobos may be a captured asteroid and recent discoveries are changing attitudes:
"Yet new information is already pouring in. What scientists have discovered is already starting to transform our understanding of Rosetta's target comet, 67P/Churyumov-Gerasimenko (C-G for short), and cometary science."
1. C-G looks nothing like we'd expectWhere's the ice 3 surprising comet facts we've already learned from Rosetta
2. The surface is hotter than we guessed, and surprisingly ice-free
3. Despite its dry surface, C-G expels an astronomical amount of water... but not on its dark side