As someone who has also lived in Greece I certainly understand the kind of reaction you have had from your Greek neighbours and have experienced it myself.
When we were there, we treated our dogs in the same way as we do here in the UK - in other words, both of our dogs lived in the house with us and were treated as part of the family. This was quite astonishing to many of the neighbours who were worried that the dogs would have fleas and diseases that they would pass on to us. Of course, we made sure that they didn't by getting them vaccinated, wormed and treated for fleas and ticks just like we do here. This was a bit of an eye-opener to the neighbours because they had simply never considered that this was an option (at the time, there was only domestic vet on the whole island).
In many ways, I found their attitude to be very much as KC put it - most of them have animals for specific jobs and, in the majority of cases, that is where the human/canine relationship ends. They wouldn't go out of their way to treat the dogs badly but neither would they sit on the setee cuddling them like we do ).
We were aware that there was some poison set down in various places around the village - it is often used to keep the local vermin under some sort of control - so we tried to make sure our dogs didn't go off scrounging in case they came across it. Of course, it isn't possible to keep your eye on them all the time without locking them up and we chose not to do that, so maybe we were particularly fortunate not to have one of them get into trouble.
I guess that is one of the parts about living in Greece that you have to come to terms with if you're going to make it work. By all means, we can try to help the neighbours see there is an alternative but we shouldn't expect things to change overnight. After all, if too many things changed about them, would they still be the same people that we like so much?