My understanding of nematocytes is that we don't get stung by most because they are not able to penetrate our skin. They still pack a serious punch (as attested by the coral wars you observe in your tank), but typically pose little threat to us. If, however, you have a cut, they can inject the venom directly into the bloodstream.
Not that it really matters, but I would propose a different theory than zoas theory for a couple of reasons... I suspect a zoa would not cut you, but more so because the symptoms of palytoxin are more typically less localized (I have two good friends give me first hand accounts and have done a fair bit of reading on it since). I would bet the coral you pulled out of the cut was stoney?
As for the Vinegar, the medical profession and primary literature seem to be in agreement that it is recommended as a treatment for most jellyfish (and I would assume coral) stings. The vinegar deactivates the nematocytes, allowing the removal of the jellyfish tentacles (or coral chunk) without further triggering. Urine, however, not so, although you are welcome to try...
Dan