The more pipes you have, the more pipes are available to fail. That includes a water line for a fridge.

That said, a properly installed line using quality materials is not going to break. Ever. Period. Regardless of whether it's for an ice maker, drinking water, water filtration, instant water heater, whatever. Risk factor of the line itself should be no more than any other plumbing pipe already in the house. In fact it may even be better (you can't inspect what's already in your walls and floors.

Ok, you may want to replace the line if you've installed it 20 years ago. But owning a home means inspecting things like that once in a while.

As far as the fridge itself springing a leak... Well, that's a different story entirely, but again, not significantly more problem prone than any other plumbed fixture. If your fridge is a lemon you're probably going to find out right away.