I used to work at a small but successful deli right off the Main tourist street of a small historic downtown area. The owner did not take credit cards either, but had an ATM about 10 feet from the register. The ATM charged $3 for each transaction. You know damn well everyone knew exactly what he was doing- almost half of the customers would walk up to the register to pay and were then informed of the no credit card policy. Many of them protested, a few got really angry. A few refused to use that ATM and would instead walk 2 blocks down to the BoA to use the free ATM. Now a server always prefers cash tips to credit tips, the latter having to be reported as income, but I guarantee this ATM was not put there to encourage additional cash tips. As I had no metric to determine whether or not one would make more tips if we had accepted cards, I really can't say whether the policy helped or hurt the staff. I would only hope that the customers disdain for an obvious ploy to cheat people out of $3 additional dollars, in a time when taking credit cards was pretty much universally accepted, would not cause them to take it out on the person who served them.
(Granted the tips were a lot lower there than at a fine dining restaurant; a $5 tip would be considered good for a 1-top. At a nice place like where OP went, a $5 tip would be an insult- even more so than simply leaving nothing. Remember the redneck in the movie "Waiting"?)
As a former server, I can only say please, never penalize the server for something they cannot control.
Regarding that place, they likely get less charges in merchant fees when they run cards as debit. They might even have the option to take credit cards, but they just tell people that they cant to save money.
So to answer your question- so long as we have determined that is is NOT the server's fault, I would say the market dictates who is right and who is wrong here. If the majority of the restaurants in that area all accept credit, and this place is the one exception, then its their fault. However if there really is no set standard, and half do take credit and half do not, for example, then its your fault.