I don't think that's true regardless of whether you or Feynman or anyone else says it.

For example:

Every continuous symmetry of action in a physical system with conservative forces has a corresponding conservation law. (Noether's Theorem)

There must be two antipodal points on Earth with exactly the same temperature and barometric pressure (as a result of the Borsuk-Ulam Theorem)

As far as I know these are absolutely proved positively because they are mathematical consequences of the properties of continuous functions etc. I'm not a scientist, but there are thousands of things like this where we are definitely absolutely certain we are right because of the possibility of a mathematical direct proof.