Is SPEED of critical thinking important? How many positions at Google require people to think on their feet? How many positions require them to be comfortable/effective talking to strangers on the phone (for this woman's position, it might be the case)?
Check out the War For Talent ( https://www.amazon.com/dp/157851459 )... Andrew Chen has a good blog post talking about it: http://andrewchenblog.com/2009/07/28/what-if-interviews-poor...
Bottom line is that studies show over and over that "if you look at the marks that people get coming out of a hiring process versus the on-the-job marks they get in their first year in a job, they are actually not correlated at all."