This is very hard for me to confirm: I don't have any crt close by and the crt's which I used more (late 90's) were already mostly plane.
But I remember big crt tv's. Some of the biggest one's, had a form of "inverse" curvature to mimic plane panels of the time. I clearly remember one whose curvature was not constant over the screen and panning scenes had a weird effect of enhancing its deformities. So, I still think he is wrong even on this second case.
However, it's probably not as extreme as what this does, and when you're sitting in front of it (the photo is at an angle) I don't notice much text distortion.