I have mortgage companies that will give you a mortgage based only on the cash flow shown by your bank deposits. That's a totally different kind of loan program And something a business owner or self employed person might use.
That had nothing to do with the issue of tax returns. If you are submitting tax returns they will be verified, just as banks will verify your checking account statements if that's the loan program you are applying for.
There are ways for a gambler to get a mortgage and again the easiest way is with a substantial down payment for a "non qualifying loan" which simply means there is enough equity in the house that the lender will assume the risk you won't go into foreclosure.
It works with car loans too. If you have no credit but put down a big down payment of 50% anyone will sell you a car.