I feel that she makes some of the same mistakes as the people that she criticises.
For example, some conservative Muslims will claim that more liberal Muslims aren't "true" Muslims. People of faith often claim that others with a different type of faith don't have "true" faith. It's often an attempt to hijack the meanings of words to advance their own view. It makes any meaningful discussion difficult. It is often easier to subvert the meanings of words used in a debate than to use rational arguments.
She does the same thing by making up her own definition of faith and then claiming that others who actually have very strong faith don't have "true" faith and are infidels.
I think it's needlessly offensive and just silly. It appear to me that she is working under the assumption that faith is inherently good, so anybody who has a type of faith that she feels is bad doesn't have "true" faith.
It's much more practical to realize that faith, as it's commonly defined and understood, can be either good or bad depending on the situation. Some of the broader definitions of faith can include the possibility of doubt. In any case, I would generally regard it is a positive thing for faith to be tempered by doubt. However, to claim that doubt is essential for faith just doesn't make sense. It perpetuates the dangerous myth that faith is inherently good while making future dialog on the subject more difficult.
I believe in the value of doubt. It is often a great virtue. I just think her defense of doubt is flawed.