The term you’re looking for is “overhead” and “speaking fees”. It’s very surprising just how profitable a non-profit can be, especially for the person running it.
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Keep in mind that those are average salaries across particular percentiles in a particular state, but it demonstrates the point. You don’t have to exchange money under the table - you can just say it’s part of your operating cost, job done. Everything depends on how big the organisation is and how high up the ladder you are. It’s not uncommon for non-profit executives to earn upwards of a $100k a year just in salary, and orders of magnitude more in speaking fees, which is no chump change. Now, I am the last person to criticise someone for making a profit - good on them, but I have the uncanny ability to detect scams from a mile away, and that there is a scam.