Cash out refinance vs refinance: different LTV allowed?

[Tucker Long]

I was told the following, could someone confirm or deny this is accurate?

If I pay cash for a home, rehab, rent, and go to refinance Fannie/Freddy guidelines will require me to keep 20% equity/my own cash in the deal regardless of new appraised value.

If I buy a home with hard money/private money with a note in place, rehab, rent, and go to refinance I can put 80% LTV in place based on the new appraisal. So potentially could have none of my own capital in the deal if I buy right/add enough value.

SO basically, they were claiming there's an advantage having a first mortgage in place when completing a BRRR because it allows me to leave no skin in the game, where as if I buy and renovate with cash I'll be forced to leave 20% or so in the deal.

Thanks for any thoughts,