That's not what the lady said. She said that after the ice age and before the impact, there were really simple things like algae and bacteria and stuff, and no evidence of diversification:
"As the sea level rose at the end of the ice age, these spherical forms increased in number," Dr Grey said. "But there is no sign of a new species emerging at the end of the intense ice age to support ideas of the rapid diversification of life at this time."
Only after this asteroid impact did all this new spiny stuff supposedly show up.
Now, both the ice age and the asteroid were associated with huge extinctions, but only the latter produced the rapid mutation. Given that the same beasties were supposedly around in each instance, we'd expect either to have seen mutations after the first extinction, too; or no mutations after the impact.
These researchers appear to be saying that it was something about the asteroid that made the difference -- hence my reference to Hoyle.
There was no selection pressure favoring the new mutants. They were born and died out, ending their genetic influence, or limited to very small populations who didn't happen to leave a fossil record.
When conditions change, those few mutants who earlier may have had relatively expensive requirements compared to their simpler cousins, suddenly had a survival or re-population advantage.
I think you'll find that most higher complexity organism have initially higher "expenses" and therefore have a hard time getting a toe hold in a well settled niche. But when something comes along and upsets the apple cart, those few who've managed to pay that initial expense can now exploit that capital.
Complexity of organization requires an initial investment. Simpler organism can get into production quicker, and so tend to win the early races. But they are often less robust in the face of changing conditions. The more complex creature was paying for some unused abilities, and suddenly that is the difference between life and death -- or at least speed to repopulate.