Of course this can happen in any country, and why not in Cyprus!!
So, if you don't want to fall in the trap and pay much more for a ride, spend a few minutes and discuss clearly where you want to be taken. Be sure that the driver knows exactly where to drop you off and if you agree then do show that you trust him.
Talk to him and create a friendly mood, tell him what he really wants to hear....like how much you love Cyprus, etc etc, and you will see that both of you will feel relaxed.
On my two recent trips to Cyprus I met tourists holding their guidebooks with info that was wrong.
Every evening we used to exchange our day's activities and I heard them complaining about how wrong the guides are.
Don't rely so much on the info you get from books, but as soon as you get to the island visit a Tourist Office and get the most recent leflets from there. They are given free.
Unique Suggestions: Ask locals to help you and guide you instead. They will be pleased to offer their help believe me.
If you need help with your car or lost your way, just approach some locals and you will immediately feel the difference. You are no more alone here! Almost everyone can speak English, but even those who don't speak can understand ....many of the older locals used their hands a lot to express themselves!
Fun Alternatives: Photocopy pages with info you get from reliable people who know the place well, take phone numbers with you as you might need to call somewhere to get a piece of information while on the island.
Say a thank but don't try to give the locals money. They will not get it.