Running for your life and then doing nothing about it for 37 years is a strange definition of "property held".

And I'm still not exactly sure what you mean by adjectives like "real" and "legitimate". A principled arbitrator would need to determine on a case-by-case basis who has the best claim to any given property given the facts presented. If the facts lead to a conclusion that the original owner has in fact abandoned the property, then it was available for homesteading.

It would also be expedient for an arbitrator to satisfy all parties to the greatest possible extent. In the hypothetical case I've already discussed, it might be accomplished by having the homesteader compensate the abandoner for profiting from eir loss. The amount of compensation would depend on, among other things, how long ago the events took place and how active the abandoner has been in reacquiring possession.

Edit: It would also hugely depend upon whether the homesteader was involved in chasing out the abandoner. In my hypothetical, I've been assuming that it was someone who came in after the fact.

Also, I'd like to hear your answer to the question. In simple terms, do you believe the Turks and Israelis to be the legitimate owners today?