Anyway, it's false. Completely false. There is actually a branch of science that concerns itself with cold-blooded animals and how they react to heat changes and one of their scientists, Dr. Victor Hutchison, has been widely quoted as calling this a pure myth. Believe it or not, scientists have actually performed this experiment only to see the frog jump out of the water when it was uncomfortable. (Reportedly, one of the scientists got frustrated and immediately went home to work on a new illustration for his Sunday School class.)
"Hmm, it's getting hot in here, I wonder if I should leave? Nah, I'll wait it out and see if it gets better. I wonder if these garlic cloves should worry me?"
The message, however, is still true. When it comes to irresponsible behavior people do tend to start small and work up to the really big mistakes, but we'll have to find a better analogy. If you know any good alternative stories that exemplify this part of human behavior let me know in the comments. Until then, be a frog; if something is wrong, even just a little, do something about it and don't wait until things have gone too far.