I wouldn’t say that TDI cave courses are not being accepted in Europe. OK, let’s say that many American associations are not respected, as Jago wrote why, but let’s admit that no matter on association or standards, the most important is the instructor who made course for you.
If providers of diving in caves don’t know you, or your instructor, you might have problem with TDI certification in Greece. The reason is simple, due to the local law (at this moment I am not sure but I think it is the 3409/2005), as a diver you have to be holder of diving license of recognizes diving association. And to be recognized diving association the local representative of association has to pay to Greek government every year some fee (I think it is around 5000 Eur).
TDI/SDI has no representative in Greece, that’s why it is not recognized in Greece.
In Czech R. it is bit different. All activities in caves are controlled by §10 of Code n. 114/1992 Coll., about the protection of nature. The goal is to protect and preserve caves. So for the caves exploration, there has to be the permission of the authority for nature conservation and landscape protection or from the Ministry of environment.
The basic units of Czech speleological society, who are holders of such kinds of permissions, are responsible for all activities in "their" caves. And they are following the safety standard of Czech speleological society (such as wearing helmets on heads. Just imagine what would DIR divers say about wearing helmets.). So it is on their decision, to let anybody dive in "their" caves. And of course they prefer to reduce any risks by not letting unknown divers (unknown for them) dive there, or by preferring divers, who passed course in similar conditions to Czech caves than divers who passed course in Cennotes.