It is only true in the European Union, not in whole Europe, but you are right with that. Though it's more complicated to utilize than it sounds. The main difference between the usual 1 year warranty given by Apple and the guarantee (2 years long based on the european law which bounds Apple as well) is, that under warranty you don't have to prove anything – if the device fails (for any reason), the manufacturer (Apple) has to replace/repair your product unless HE can prove that the failure was caused by a misuse by the consumer.
On the other hand, after the 1 year warranty period, Apple is still bound (at least in the EU) to replace/repair your product in the 2 years guarantee–timespan, if the error was already present at the time of the manufactere. That is, the defective quality of the flex cable which causes this problem for everybody, so so far we are good... but here comes the tricky part... the consumer has to prove that the failure was due to an error that was already present at the time of manufacture... 😟 That is something which is quite impossible to do for us right now, a legal action against Apple (or the distributor) would be needed, and the outcome is doubtful at least. Unfortunately it's not that easy that I walk into an Apple Store (or into a T-Mobile store, because we don't even have Apple Stores here in Hungary, we can only validate our warranty through the mobile network operator where we bought our iPhone) and I say: hey, based on the european law I still have 1 year of guarantee left, replace my phone right now.
So unless Apple admits the macufacturing defect and calls a world-wide replace program (which I highl doubt at this point where they don't even sell the iPhone 5 anymore – suprise, surprise, they turned their back to their faulty product instead of fixing its problems), that's all folks...
By the way right now my power button hardly operates anymore. Two weeks ago when the symptoms started it was at least usable if I pressed the left side of the button, right now it's almost completely unresponsive. I give it a week until I'll have to turn assistive touch on. Yeah, shame. Not to mention my other problem which I noticed a few days ago (rear camera having purple "dust" between the lens, which affects and ruins picture quality – also a glitch that a huge number of people are having with the iPhone 5; see it here) So, yeah... I'm starting to wish I had never replaced my good old iPhone 4 which was opreating flawlessly for a good 2 years. Good old times...