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TL;DR: This group of players does not like you running the game with such a firm grip. Regardless of who is right, you'll need to give them back some control by letting them reach a consensus in these cases, or risk losing the group's interest.

People have listed some decent conflict resolution tactics here but I think a key point needs to be emphasized a bit more. It doesn't matter who is technically right in the situation, the problem is that the whole group was against you. At that point the game is not living up to the players' expectations and you should either bend to their will and let the argument go, or at least (if this is the case) say "I'm sorry but that broke my plot" so they understand where you're coming from and then try to reformulate on the fly with the new mechanic in mind.

If it were just one player being a pain then a GM ruling might fix it (though that player may leave), but if the whole group is erupting with complaints you've got a much more serious problem on your hands. It sounds like you're not running the game the way they want it to be run, so if you want to continue with the group you'll probably need to be more flexible in these situations whether you agree with it or not.

Spend a couple minutes letting both sides make their cases, and if they're still convinced you're wrong, ruling against them all is only going to destroy their trust in you. If you want to keep this group you might need to apologize and establish a dispute resolution method that gives them some amount of power, otherwise they are probably going to quit or at least not have fun anymore. I think your ruling is technically right, but a lot of players these days don't appreciate such a stern approach to handling disputes. The "GM is God" rule is very old-school, which is fine, but only if that's what your group expects (after all it takes an enormous amount of trust and respect) and it sounds like they don't buy it.