The certainty of a calculation still depends on whether the quantities describe the right situation.

Precision inside a calculation says nothing about whether the calculation is about the right thing. The arithmetic can be flawless while the numbers you fed it describe a different situation from the one in front of you, and the confident output will not warn you. Rigour protects the process, not the premise.

Before trusting a result, check the inputs against reality rather than against the model. Ask what each quantity actually refers to, when it was measured, and whether the situation has changed since. The most expensive mistakes usually pass every internal check and fail only against the world.