Imagine if they only made short guys pay to get in, and you or your short friend were told to pay.

If that's how it always worked, and I knew I was going to that sort of place, I certainly wouldn't throw a fit when it happens, or expect everyone else to abandon their plans for the night. Whether you find the whole process of getting into a club problematic or not is beside the point - it's how it works, so the time to make that decision is before you go. I understand if her feelings were hurt, but expecting everyone else to play to your sensitivity over an entirely foreseeable situation is pretty obnoxious. The group offered to cover the cost for her, so all that was really at play was a blow to her ego that she could've guessed was coming - hardly a reason to cancel everyone else's plans.

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She can take them up on their offer, sulk a bit, and try to have a fun time, or she can throw a fit and leave, but the offense isn't anywhere close to great enough to alter the full group's plans over.