Being 'data-driven' does not mean that you should use bad data.
Relying on data rather than intuitions to make decisions is usually a good thing, but is not always better. When one needs to make a decision about things for which there is no good data it might be better to rely on intuition rather than the best proxy available. Here are some examples where I think an intuition-based approach can be better than a data-driven approach (but still worse than a data-driven approach with good data):
Stock market
Bad intuition: "how good does company X seem"
Bad data: "what were the returns on X's stock last year?" (remember: past performance does not predict future performance)
Better intuition: "do I have a compelling narrative about company X and a reason why external investors might be mispricing it"
Better data: complex quantitative model (the kind you might not create unless you work in finance though)
Train delay (in the UK)
Bad intuition: trains are usually on time (reason about the mode)
Bad data: look at the currently published delays on National Rail's website (these tend to be overly optimistic)
Better intuition: use "what fraction of times have I experienced a delay in the past" as the estimated probability of a future delay
Better data: actually track and calculate this number (clearly doable but more work than most people would want to do)
Accepting a job offer
Bad intuition: how good does field X seem.
Bad data: look at average salary/work hours/satisfaction for people in field X.
Better intuition: does the team/manager/work environment at the company that gave you an offer feel "right"?
Better data: get data on salary/work hours/job satisfaction for your prospective company specifically (usually hard to get this data though).