Well it is similar to open source. Just making a project open source doesn't automatically reduce the number of bugs. People need to be interested and capable

Well it is similar to open source. Just making a project open source doesn't automatically reduce the number of bugs. People need to be interested and capable of auditing it. However, even if only a small percentage of people do audit it, the gains from that apply to everybody. I think it generally works out. More popular open source projects naturally have more eye-balls, which means more people auditing it. Similarly with sharing data, more controversial or interesting claims will naturally attract more attention and therefore more people who are capable and interested in verifying the claims.