Keyword is "measurement error." People think hard about this.

People like engineers and physicists think a lot about this. I am not sure that medical researchers think a lot about this. The usual (easy) way is to throw out unreasonable-looking responses during the data cleaning and then take what remains as rock-solid. Accepting that your independent variables are uncertain leads to a lot of inconvenient problems (starting with the OLS regression not being a theoretically-correct form any more).

What you see might be different from the underlying truth in systematic ways, e.g. you get systematic bias in your data, and you need to deal with that.

Yes, that's another can of worms. In some areas (e.g. self-reported food intake) the problem is so blatant and overwhelming that you have to deal with it, but if it looks minor not many people want to bother.