When people lie, it is usually easier to catch them, as most falsified data has illogical elements.
It is better to have a registry of people killed by police and vice versa than not to have it.
Even if your data has flaws in it, the average will point toward the truth.
Take elections: there has almost certainly never been an election in which there were not some mistakes and flaws: noncitizens voting, qualified citizens refused the ballot, and many other types of errors.
But if you have six million Americans who vote that they prefer candidate X to candidate Y, it is far more accurate than just proclaiming X or Y to be president, senator, representative or whatever.
Things are not as they appear: the Earth appears flat, The Sun appears to travel across the sky. It is easy to conclude that a metaphorical deity is crossing the sky daily in his fiery flying chariot.
We discovered that this is not so only when we began collecting data, and then analyzing it.
All wide ranging data will have imperfections.
But imperfect data is still better than no data at all.
At present, we have no data at all.