I absolutely agree about kids these days often lacking a solid foundation (in part because electronic devices make it so easy not to learn it). And I don't think knowing the why of simple multiplication is all that critical for many kids. I don't think that was a great example to use - nor a great example for the media to pick on. But I do think it is important to be able to show kids how and why stuff works, and for kids (students) to be able to explain their understandings of things.
Actually, examples of why basic multiplication works is as easy as using tactile objects or graph paper...three rows of four, stacked in a rectangle... three squares down the side, four across the top.... make it pretty clear that 3 x 4 is neither 11 or 13.
Math, like sports, is all about accuracy. The final answer is what we want. But to say that a kid doesn't understand a given concept because the final outcome "ain't right" can be incorrect. Sometimes you have a team which knows the game well, knows lot of good techniques and understands the plays well, but simply doesn't win many games. A good coach might recognize a couple simple things that move that team from a losing team to a winning one. In the same way, if a kid understands a certain mathematical process but fails because of an error along the way, it pays to know why. Otherwise you may just be beating a dead horse by repeatedly showing them the same concept over and over. It is possible to give a student credit for understanding of concepts - if that's what you're trying to teach them- even when the final answer is wrong. Then it's time to go to work on where they struggle with the problem of errors. (And lots of times there are fundamental issues with failure to know basic stuff very well, part of the reason I think a basic multiplication problem was a poor example for the presenter to use; perhaps she was an elementary teacher, perhaps she was a math teacher talking to a group of varied content teachers, not all of whom might remember polynomials or whatever, had she used that for an example.
BTW, in retrospect, yes, your answer was funny. However, it struck me as so similar to what a junior high math teacher -whose name more than four decades has erased- would have used, that I didn't get the humor at first. (She didn't do it to be funny.)