We have traveled in rural Italy and France and have not worn hiking boots. But I recently read that when exploring the rural parts of Greece one needs to be sure they are wearing hiking boots. Is this true?

Hiking on well-worn/maintained trails, hiking boots are not necessary. Making your own trails over uneven and unfamiliar terrain, yes, definitely.

Depends on the terrain, as BLL wrote. Are you planning to do some serious hiking? I cover some pretty rough ground in my Tiva sandals, but wouldn't want to wear them on a long trek. Hiking boots, IMO, are too hot to wear in summer, but might be necessary if you are doing some long distance walking. For normal sightseeing around towns and villages, exploring ruins, etc, trainers or sandals will do.

It depends on what your other shoes are like.

I went on a walking holiday with a group and we all wore boots. It can be very dry so the ground is hard and ungiving. We also, while on the walks, visited some of the historic sites in the Pelopponese. I did not feel my boots were out of place, unlike the tourists who had got off cruise ships in the most unsuitable shoes. This was walking aimed at reasonable walkers not expert in any way.

The paths are not well marked and our leader had problems getting hold of sufficiently detailed maps on occasion so you might find yourself walking on less than perfect paths.

If you are driving and taking short walks you may not need boots but I think they are sensible for a walk of any length.

what they said would hold true for Crete

Many archaeological sites have rough uneven terrain and/or slippery stone surfaces -- a mid-to-high top shoe can be nice.

I have a pair of *very* lightweight, vibram-soled, Lowa boots that I *wish* I had brought on my last trip. Next trip, the Lowas will be my primary pair of shoes, with Teva "sport" sandals as the 2nd pair.