I live and attmepted to rent out of Buffalo NY-- about an 8 hour drive from Manhatten--- so definetly not the problem.
However, they are not all the same. Around here there are 5 different
Budget locations. Each owned independently, each with different rules too. This can lead to some confusion. We found this out after renting an internet rate at a Budget about 18 months ago and we were told, even though my reservation went through, they weren't going to honor the internet rate. They said this was a problem they were having and were working on. They then told me that they were privately owned as were the other ones in the area.
As for it being there policy for 5 years with
Alamo and National--- We rent cars (we don't usually fly) from the Buffalo airport an average of 4-5 times a year. I have had the same debit/visa card for many years. We never had a problem until 2/03. This is when they told us they just changed their policy. We had just rented 4 months previous to that. Same card-- same company (and 2 more times previous to that in 2002).
Also, not all debit/visa cards are the same. Each bank decides on the appearance of the card so while "X" bank may put check cashing card on theirs. "y" bank may not. This may play a role in the card going through as well.
In my opinion, if an ATM/Visa(mastercard) is the only card you will have. Then I would call several times to the location you are picking up at and ask the question, to be on the safe side.