It depends upon what the options are. If you can demand and get good data, then people will ask for good data. If they don't think it is possible to get good data, then they may demand no data because no data is better than bad data.

For an extreme example, consider a country where homosexuality is punished by long prison sentences (or worse). Would you trust any data that such a government produced? If they produced data showing something negative about homosexuality, would you even spend the time to look at their methodologies? Or would it be dismissed as inherently biased as the source would be seen as being incapable of being trusted? For me it would be the latter.