I understand how you feel... however, I did not get the impression that the logbok was absolutely necessary in order to be able to dive with these operators. They asked for it to assess where they could bring us, I think. Being a newbie, I think it is totally understandable, and I actually like it when a shop checks what I have done.
One of our party did not provide the logbook in a diveshop in Veracruz (here in Mex) the first time we showed up there, and he was taken down to 90ft all the same for the second day of diving. The DM checked us first in shallower reefs the first day though. Now he has started a logbook, because in order to take the SSI Advanced certification he needs to log some 20 dives (I think the number is correct, but I am not 100% sure) -- he has more than those, but no log of them, just like you!
The Greek operator would not take anybody down to 100ft without AOW certification or a healthy logbook and some check-out dives with them.
Looks as if it is worth having a record!
Cheers, Itziar