They say they discourage it, not that it's banned. It looks to me that they want two things. The first is to discourage inappropriate behaviour during someone else's performance. The second, implicitly, is to encourage best practice.

"it's really nice if people can memorize every song they sing, but it just doesn't happen all that much any more". I find that statement very depressing. The pros and cons have been gone over many times, and there's no point in repeating them - that's not the purpose of your posting. I can only say that in my experience performances by singers who have taken the trouble to memorise the song (or play a tune) are nearly always better than those who read them.

There are exceptions, and you may be one of them. If you have genuine memory issues then you may be fully justified in using a prompt, and if you're sufficiently practiced you may well be able to deliver a good performance. However in too many cases it's simply an excuse for not making an effort, and all too often it is accompanied by a failure to properly understand the song or make it one's own.

As for your specific complaint, I think you are entitled to ask for your money back, especially as they only raised this after you had booked and that they should have known this is your practice - you were after all specifically invited. However it seems to me to be only a recommendation, and unless they are going to insist on it then perhaps you are being a bit 'snooty' yourself in responding the way you have. I can understand your annoyance though.