Not true at all. Blackbody radiation goes to infinity with Wien's distribution; error bars aren't going to get you there.

Likewise, our 1/r^2 understanding of forces goes to infinity as distance goes to zero, but we currently can't resolve that problem with error bars for the nucleus of an atom, where Heisenberg tells us any two protons can sometimes appear closer to each other than the "radius" of the nucleus.

You can't make Schottky diodes using Maxwell and error bars.

That is the entire problem: the classical models weren't merely inaccurate; they predicted completely absurd (and provably wrong) results at extreme scales.