Actually, statistics work in these guys' favor. It's the old defense vs. offense saying: sure, you want it to fire at that one particular second every 5 years, but the other 157679999 seconds you're sure as hell don't want it going off. It makes sense to put more effort into stopping false positives than false negatives. You might then ask, "Why have a gun if its only purpose is to be NOT fired", and then I ask, "Why indeed"? But that is a different conversation.
Guns kept in the home for "self protection" are alarmingly likely to be used against their owners, either by burglars who find them first, children by accident, or the owner himself for suicide (not that this tech would prevent that). Even the latest James Bond movie made this point, where the first time anyone pulled the trigger on his smart gun it was the (very disappointed) bad guy pointing it at Bond's head. Yes, not firing when you want it to is bad, but it is just as bad if not worse to have it fired against your will, especially in situations where it is the only firearm in the fight.
Their example of using the tech in a war zone is both good and bad, since it prevents you from being ambushed and shot with your own weapons, or stolen supplies arming the enemy. But you couldn't use them with gloves on, burned fingers or a number of other situations. A way to temporarily disable the fingerprint recognition would be a step toward your "false positive rather than false negative" idea.
That said, don't compare the reliability of this electronic gun with the reliability of a PC or cell phone. They had better be using military grade components and have a battery that lasts for years of use. And the user had better stick to whatever maintenance schedule required by the manufacturer, in which the battery would need replacing every few years. If they can't be bothered to do that then they have no business owning any kind of gun, smart or otherwise.