I once had a sensor that rounded the data, so the output unwittingly fitted into a grid. The equations that had to be used on that data gave infinite results because the grid sometimes rounded slopes into vertical lines.

So I had to reconstruct a signal that fitted the data for the equations to work at all. But the reconstruction was no longer measured data. It was made up, and there was no single solution for fitting the data. That meant I could claim to "respect the data" while producing any result I wanted.