And if the loan gets sold to the government, it needs to meet government underwriting criteria and the lender has no free will. Especially for residential mortgages: No private business cares about 3% interest on a loan, they sell those to the government and make money on the origination fees.
If you get a hard money loan, they'll only ask for tax stubs but you'll also pay 10-12% interest. If the buy is really good sometimes they don't even care about taxes or ability to repay - they get your equity if you default so who cares if you make a dumb decision? It's mainly the government loans where they really try to avoid defaults.