What is this power button you speak of? I only have a Sleep/Wake button and the Home button.

Just kidding.
I just tried what you mentioned and it didn't seem to dim at all. I have my brightness set right under the TN in brightness and the screen never dims. I do however get a random bug that lowers the brightness for long periods of time until I change the brightness via Settings.
This is on an iPhone 5 that was setup as new.