Xkcd: Statistics Tip
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Your example is not good because increasing resolution is a "let them eat cake" copout, and ignores the importance of grasping basic parameter identification techniques to figure out key parameters from real data that is available instead of hypothetical data whose recording might even be unrealistic.
Suggesting that you should start by looking at the right place and employ real or fictional equipment to get enough resolution to make the data obvious is both unrealistic and unhelpful.
I would say that that's why you need statistics. It's literally the field dedicated to reliably make sense out of data.