It's not that they weren't diversifying before the impact, it is that the existing forms were dominant under those pre-impact conditions and newly mutated forms really couldn't get a toe hold.
The impact both changed some conditions and wiped out a lot of the existing competition. And the race was on.
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.