The difference there is, I think, that the pragmatic argument of "not enough steel" doesn't prove the non-existence; while the argument about "there are no truly rigid bodies" does.

I haven't seen that Veritasium video, but it sounds like it makes the exact same point. It's not that we haven't found a material that's rigid enough; it's that a rigid disk is counter-factual to begin with, even in non-relativistic conditions.