Paying in cash absolutely helps commit tax fraud. It doesn't mean your contractor will commit fraud, but if they wanted to, it's a lot easier if you pay with cash compare to check or credit card.
That's 100% on them. I'm under no obligation to give some credit card company my personal information just so more fingers are in the pie when accusing the contractor of fraud.
Cash is good and I accept 0% of the blame of what other people do in response to me paying them with cash instead of something else.