Perhaps a Pan Pan call would have been appropriate in this case. After all, if you have determined it was a false warning then you are not in serious or imminent danger, but there is a condition affecting safety on board. ATC will make the same efforts to get you on the ground, and the fire trucks will still be scrambled, but they won't call out local civilian fire service etc.
Pan Pan seems though to not be used / understood as widely outside the UK.