At first listen, I had somehow developed the misconception that the article was saying the learning of basic math facts was not necessary to develop fluency, and that it was causing anxiety and fear in early learners. I was mistaken. After rereading the article I would say that this line best summarizes her stance: "Teachers should help students develop math facts, not by emphasizing facts for the sake of facts or using ‘timed tests’ but by encouraging students to use, work with and explore numbers."
I am a big fan of Jo Boaler's work with growth mindset in mathematics, and I agree with much of what she says about the need for developing number sense, as well as the memorization of facts not being what math is about. Check out Maths is not special for more about this last idea.
However, I strongly believe that the recall of some basic facts can be immensely valuable when learning mathematics which supports Boaler's statement that "mathematics facts are important." Specifically, addition up to 10 + 10 and multiplication up to 10 x 10 comprises some of the knowledge needed to be fluent in number sense. The author illustrates this when she admits that she doesn't "stop and think about the answer to 8+4", and in each of the cited 'number talks' multiplication facts of up to 9x10 are used as building blocks in solving the more abstract computational problems.
There are numerous analogies between learning English and learning math, so I'll throw my hat in the ring and start at the beginning with counting. Even before my daughter could recognize numbers, she was able to count, much like how she learned to talk before learning the alphabet. I like to think that learning her ABCs was akin to her learning to count from 1-20, and by 10s to 100. As she learned to read by sounding out words, she needed to be taught that c-h makes a "ch" sound, whereas in math she learned that 2-3 makes twenty-three. Likewise I think of sight words as a corollary for basic facts. As a budding reader she could sound out the word "choose" every time she saw it, but eventually she progressed to the point where it became a sight word for her. In math, when she was given 2+3 she was quite capable of counting to get the answer, but eventually she saw this as one of the "ways to make 5."
Ultimately, I think all math teachers would agree that we want our students to develop a solid grasp of the "basic facts" without scaring students off of learning mathematics. Maybe for some, myself included*, rote memorization works, but for others we need to be willing to patiently use other strategies.**
*I still remember learning my times tables in Mr. Bradley's Grade 4 class (6 x 7 was my nemesis) as well as how to write a cheque, fill out deposit/withdrawal slips, and doing enrichment with patterning.
**Feb.14 Update: Kyle Pearce illustrates this at http://tapintoteenminds.com/2014/04/13/memorizing-multiplication-tables-hurt-help/