Its called used an anecdote to illustrate the problem. This type of problem is something that survey designers have to deal with. Do you think they just slap a bunch of questions together and hand them out? You can but then you get crappy unreliable results.
"Anecdotal Evidence" is an oxymoron.
anecdotal evidence
nounA limited selection of examples which support or refute an argument,
but which are not supported by scientific or statistical analysis.
Have you ever taken a class in statistics? It’s the science of collecting, exploring and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry and government – to become more scientific about decisions that need to be made.
IMO, statistical analysis IS a science, but the information produced by this process is, itself, not what I consider scientific. 10 people can analyze the same data or conduct the same surveys, and they can all get different conclusions. Need an example? How about the 2016 Presidential Election polling. Need another? How about the 2012 election.
Based on specific characteristics of the datasets, the way it was collected, the expected distribution of responses, etc, etc, etc, you pick the METHOD that best represents the dataset.
Basic Statistical Analysis Methods:
Regression
Standard Deviation
Mean
Sample Size Determination
Hypothesis Testing
/and more/
Depending on the method selected, the margins of error (how many people lied, didn't understand the questions, gave simple answers to complicated situations, etc.), would compensate for responses like the "rape-not-rape-lie" would be accounted for. In the final analysis, the predicted results are guesses and estimates. You can't really use the numbers as absolute or exact counts, because one of the purposes of the science is to take a sample of the population and extrapolate it to describe the whole population.