Both posts are describing different moments in the same deal, and the confusion clears up once you separate entry from exit.
At entry you need the whole purchase price plus the rehab plus the carrying costs, either in cash or borrowed from a short-term lender. Round numbers: $100,000 purchase, $30,000 rehab, $10,000 in closing costs, taxes, insurance and utilities while it's empty. That's $140,000 you have to produce before any of it comes back. So the $50,000 post is closer to the truth about what it takes to start, and the no-money-down framing is describing what the deal looks like after the refinance rather than before it.
On your second question, you can refinance a property you own free and clear. It's called a cash-out refinance, and instead of replacing an old loan it just places a new one and hands you the proceeds. If the finished property appraises at $180,000 and the lender caps cash-out at 75% of value, that's $135,000 of loan against your $140,000 all-in. You'd have $5,000 still stuck in the deal and a mortgage payment you didn't have before.
The part people skip: that $135,000 is borrowed money, not profit. The rent now has to cover a real payment plus taxes, insurance, maintenance and vacancy, and in a higher-rate market the payment is larger for the same loan. Lenders also usually make you own the property some months before they'll lend on the new value, so ask any lender you talk to what their waiting period is and get the answer in writing before you buy anything.
