There is an amazing lack of understanding of what being a 501(c)(3) non-profit means. Non-profits most certainly can (and regularly do) invoice for services rendered. They are not "non-revenue" corporations, simply non-profit.
There is no fraud involved if a non-profit performs services in return for an agreed fee, or contracts to perform those services in the future in return for a fee either paid up front or after the services have been rendered.
The only thing the non-profit cannot do is take the surplus funds over and above their expenses at the end of the year and distribute those as dividends or ownership distributions to its "shareholders" or board members.
Now, if the non-profit has what's called "unrelated business income," that is income generated from activities it conducts that are not really connected, other than financially, with its mission, then it may have to pay taxes on those (for example, if a non-profit devoted to supporting a university buys commercial property as an investment, and leases that property out to businesses, that rental income may be "unrelated business income"). But that does not destroy their non-profit status for the rest of the funds they receive.
This is not, of course, definitive tax advice, but your post is about the 10th in this thread I've seen that has the very, very, very wrong idea that being a 501(c)(3) means you can't charge for services provided. They can, and they do all the time.