I wholeheartedly agree that calling videography "filming" is both inaccurate and annoying. (And don't get me started on how people misuse the word "ironic".)
But the idea that film is durable comes with a lot of caveats. Sure, it lasts a long time if properly stored. But many of the movies that TCM airs aren't really "classics" in the sense that they're especially good. They're just old movies that have survived for a long time. There are hundreds - maybe thousands - of films that we can only read about because they're gone forever.
It's also true that up until recently, video was even less durable. But digital video can now be copied perfectly, with no generation loss. That alone makes it more durable than film. It's easy to forget how recently this trend of digitally projecting something that's never been on film really is. The technology has moved extremely quickly. I think it's very possible that 20 years from now we'll look on this transition phase as an era that both film and video aficionados will look back on with awkward pride.