The fact that you can't "do any sort of reliable or trustworthy background check on every account through the app" is what justifies charging money. Something

The fact that you can't "do any sort of reliable or trustworthy background check on every account through the app" is what justifies charging money. Something that can be done purely in software by the app should be free. That could mean verifying that the user has control over a web site, or that they use Android, or that phone location services places the user in a particular city. Cheap things would include credit checks and other simple background checks. Registered mail could be used for addresses. Property records could be looked up. Educational transcripts could be obtained. Some verification could involve a notary public. Since the user would be paying for costs and a profit, there really is no limit to how complicated and expensive things could get. If the user wants to pay to fly out a team of investigators, that is fine.