"Ms. Payette is undoubtedly a very intelligent woman."

Yes, that is likely true.  But intelligence is not the same has being sensitive to others and possessing good (political) common sense.

"She will learn from her gaffe and will move on."
Perhaps.  But that is a large assumption.  I made the same assumption repeatedly through the first year or so of the current PM's tenure.  "Oh, he will learn..." (on the FN file; on thinking before speaking; on making appropriate choices for cabinet and other positions. Perhaps like the GG.) I'm still waiting. 

Her subsequent speech extolling “tolerance” and “freedom of religion” shows that she is trying to do that.
Not necessarily. All she's trying to do is the ol' back-and-fill, probably in response to a tip from the PM through the PMO, perhaps. That's all.