It's not precision that's the problem, but understanding when something has been falsified. For instance the Lorentz transformations work as a perfectly fine ad-hoc solution to Michelson's discovery. All it did was make the aether a bit more esoteric in nature. Why do you then not simply shrug, accept it, and move on? Perhaps even toss some accolades towards Lorentz for 'solving' the puzzle? Michelson himself certainly felt there was no particularly relevant mystery outstanding.
For another parallel our understanding of the big bang was, and probably is, wrong. There are a lot of problems with the traditional view of the big bang with the horizon problem [1] being just one among many - areas in space that should not have had time to interact behave like they have. So this was 'solved' by an ad hoc solution - just make the expansion of the universe go into super-light speed for a fraction of a second at a specific moment, slow down, then start speeding up again (cosmic inflation [2]) - and it all works just fine. So you know what we did? Shrugged, accepted it, and even gave Guth et al a bunch of accolades for 'solving' the puzzle.
This is the problem - arguably the most important principle of science is falsifiability. But when is something falsified? Because in many situations, probably the overwhelming majority, you can instead just use one falsification to create a new hypothesis with that nuance integrated into it. And as science moves beyond singular formulas derived from clear principles or laws and onto broad encompassing models based on correlations from limited observations, this becomes more and more true.
[1] - https://en.wikipedia.org/wiki/Horizon_problem
[2] - https://en.wikipedia.org/wiki/Cosmic_inflation