"you can't construct a peak from a plateau, that's just making thing up."

no.

it's what statisticians do - they look at messy raw data and they analyze it for errors and biases to try to reconstruct a reflection of reality from it.

the best way to explain this to a non-technical but educated audience is actually to bring in the allegory of the cave - the data is really shadows on the wall, and what we're tasked with is a way to figure out what's going on by analyzing those shadows.

if you insist otherwise - that the data is reality, and analysis is just making things up - then you are essentially the prisoner shackled to the wall, that can't see things for what they really are.