I doubt there is a worldwide statistics.
The accidents, where actual fire broke and did cause significant damage will be well known and listed on the aviation safety network. However the precautionary evacuations that turned out to be false alarms and when nobody was seriously injured may fall through the cracks and not get reported anywhere. They should be reported to the overseeing safety board and that usually publishes at least summary list, but the system works better in some countries and less in other . And there is no central store for these reports in either case, so you could try to collect the numbers for one country (according to , the reports are probably most complete for Canada), but that will be too few cases for decent statistics and worldwide data will be incomplete to the point of being useless.
However, I am pretty sure the balancing is right. Not only do fires happen, but when they do, they are fast. The China Airlines flight 120 at Okinawa on Aug. 20th 2007 burnt down in about 5 minutes. The first explosion occurred just few seconds after the last passenger left the plane and while the flight crew was evacuating. So if they waited any longer, it is quite likely someone would have died.
In contrast most evacuations don't result in injuries and the few cases are mostly bruises, some sprained ankles and if someone has really bad luck, some broken leg or hand.
The broken bones (and not sure, but I think even the sprained ankles) count as serious injuries. So that's the options the captain is comparing. If they command evacuation, somebody might break a leg, but if they don't and the fire is real, somebody will die. And they must decide in couple of seconds for the evacuation to be successful. So they would obviously err on the side of caution and command the evacuation if they have a good reason to think there might be a fire.