Garbage data is still data, and data (garbage or not) is still more valuable than a single anecdote. Insights can only be distilled from data, by first applying those controls you mentioned.
Or you can apply the Bezos/Amazon anecdote about anecdotes:
At a managers meeting "user stories" about poor support but all the KPIs looked good from the call center so Jeff dials in the number from the meeting speaker phone, gets put on hold, IVR spin cycle, hold again, etc .... His take away was basically "if the data and anecdotes don't match always default to the customer stories".
