(image via reddit)
On the one hand, what these educators are doing is playing cheap language tricks, which is revolting. Try paying them 4 dollars instead of 100 and saying that you took 100 to be a binary number, and why would they assume that it wasn't — and see how well that will go.
On the other hand, what has bothered me about the two plus two example is that I have no idea why it equals four. I have zero knowledge of number theory, and the only reason two plus two makes four for me is because of the set of elementary arithmetic equations, almost nursery rhymes, memorized since childhood (plus, there's also finger-counting for the moments of extreme doubt). Alternatively, I can think of the two plus two makes four as an a priori knowledge, similar to all bachelors being unmarried men. Not a particularly comfortable place to be, when considering foundational truths.