Right, but it still follows the same concept. It's people, without much life experience, nevermind supernatural, becoming better than deities who are thousands of years old, in only a few days.
Which is why I, personally, prefer my idea; it gives the characters a sense of accomplishment, by surviving each day, but it's pretty explainable within any world that somebody could avoid detection, if they were to try hard enough. And, if they happen to gain power through it, they earned that power by using the skills they had, and it makes every power they gain so much more sweet.
Just seems like a more fulfilling experience to me, y'know?