I am Frank from Germany, living in Mani for over 30 years. I have a story for you which is as true as it is unbelievable.
3 years ago, I went to Sparti General Hospital for a little operation. Everything went fine, I was looked after, no complaints and NO fakelaki - maybe because my private doctor was good friends with the surgeon... I had to stay in hospital for 3 days.
I have no general health insurance, but a private one for hospital. For the 3 days a paid 234 € cash to the hospital, including the operation and everything. The receipt for this I handed in to my insurance agent, to get the money paid back. 2 weeks later she called to give me a check over 703€!
My insurance paid back: the 234 € for the hospital, 69 € (23 per day) for me, and 400 € for the doctor's fakelaki!!!
This shows how deep the fakelaki system is established and how normal it is in Greece.
Generally I can say that I never got used to the fakelaki system, but I also never needed it. I have the impression that, as a foreigner, speaking the language and being a bit persistent, you are maybe helped better by the authorities than the local people.
One time only I gave a bottle of Whiskey to somebody in the Gythio tax office, as a present AFTER he had helped me out. And this was very helpful at the next occasion...
P.S. A few months ago I was back to Sparti Hospital for a 10-minute surgery. I was charged 150 €, but everybody, including the leading doctor, was very helpful to fill out and sign the fake papers for a 2-day stay, so that i could claim it back from the insurance (this time without a bonus...)
I love Greece and its people!