I think that every agency in Panamá City - not just the airport - was like that over the holidays. Last week, National, Hertz, and Avis all backed out on my confirmed reservation, and I ended up taking an Uber to my hotel, and getting a decent enough rate the following morning from a Dollar location in the city using expedia, with airport drop-off.
Kia Sportage AWD with a pissy 1.6L engine and 60k KM for $60/day including all insurance. Not the greatest I've gotten, but with every single insurance coverage, not unreasonable. Especially since I returned it with several new scrapes and in need of front end work. Shockingly good on gas too - only cost me $30 to fill the tank.
At least your rental car companies told you they can't hold your reservation...At a minimum a few days early payless should have emailed me to tell me they couldn't keep my reservation. I never got an email. When I came back to the airport 5 days later they still had a sign up that they had no more cars. What is the point of a reservation system if they don't hold the car. It is ridiculous that they over book and don't care what happens to those who had a reservation (at least when the airlines overbook they give you a voucher or credit). Their mistake ended up costing me hundreds of dollars more and their attitude that it was my fault doesn't fly with me. The Payless agent also made an asinine comment to me that "to bad you should have booked multiple reservations" which added insult to injury. In addition I submitted a formal complaint to payless 14 days ago and I haven't hard a peep out of them. Great company..
On another note sorry you had a crappy experience too.