Nonsense
It is rather standard to get a Invitation letter to many countries, CO are not gonna hold that against a person, More than likely they will never see any documentaiton since from what I have seen and experiened they don't take supporting documents.
There is no need for a somebody to be "wealthy enough and self Sufficenent to make a trip and go back home", Many parents come to USA on tourist visa and children pay for it. CO knows that. They even asked my MIL who was paying for her trip from Philippines, and she her daugther.