Most likely it didn't crash the computer, but it's entirely likely the Flash froze the browser, which could have sucked up the computer memory giving the impression of a computer crash. I've had this happen on stupid coding mistakes. To quote the cliche, "my bad."
My first guess is just that, an infinite loop or memory intensive process could have brought this about. The help files have a lot to say about optimizing memory - a Flash with lots of blends and transparencies can eat up memory very quickly. Sloppy coding can do it as well. For example, if you were to create a slide show that creates objects on the fly, and doesn't completely destroy unused/invisible objects, the Flash will run slower and slower until it freezes the browser. Again . . . sadly . . . from experience.
But in your case, since you said updating the Flash fixed it, it's most likely something being used by a later version that's not supported in older versions - for example, ActionScript 3.0 played on a player that only supports ActionScript 2.0. Ordinarily it just won't "work," but it's entirely possible it was trying to and encountered some method that wasn't supported.