The work around was a Mexican bank was the owner and lease it to the foreigner.

Know this: the #1 reason why landlords fail - failure to manage to the lease (source:  American Apartment Owners' Assn). 

I want to know that the cosigner can afford the rent on their own if the tenant fails.

You might find a local credit union or community bank that will go to 95 -100%.At one point I called 2 different VA Regional Loan Centers regarding this section in the VA lenders handbook:Assumability - The second mortgage should not restrict theVeteran’s ability to sell the property any more thanthe VA first mortgage.

I can't help but feel that some of the failed programs might offer even better opportunities than the successful ones. 

I bout one in 2019 and it has turned into a gem for me, but at the time, it would not have been 1.25 1.25x is a very common DSCR for a bank.

This is a FREE service provided by the bank, and we have used this account for about 15 years or so. 

-Local banks were the best.

It was one of my first claims and I learned how their claim system works and never failed again. 

Local banks and smaller credit unions are most aggressive in this space.