I'm from Germany and haven't been to the USA in a while, but it seems to me that working as a waiter in an expensive US restaurant is a pretty well-paid job given the percentage of tips (and considering that very little formal education/training is needed). If I eat a three course meal, the waiter basically has to do the same amount of work, regardless of whether the food costs 30$ or 100$. Of course, I expect a better/more experienced service at the 100$ place.

Regarding the original question of the thread:
In that case (assuming the OP hadn't reserved a group table in advance) I think that it was the OP's responsibility to be able to pay the bill. It doesn't seem unreasonable to be able to pay 30$ in cash or cheque, especially if there has been a sign on one of the doors.

On the other hand, if one reserves a table for a larger group, one should be informed in advance about a cash-only policy: I once took a group of students to a restaurant as part of a company recruiting event. When I reserved a table for 10 people under the company name, I wasn't told that the restaurant accepts only cash, which is quite unusual in Germany (often restaurants take only one or two credit cards, but they usually take at least a bank (EC) debit card). This was clearly stated on the menu, but of course by that time it was a bit late. The bill was above 500 EUR. Luckily, the owner operated another restaurant a block down the road, which also didn't take credit cards, but accepted my bank debit card. I had to go there with the waitress and gave her a normal tip, since she was most likely not the one who took my reservation by phone. However, I will not go to this restaurant again with a group (even though the food was good).