Having lived in Russia and Ukraine, I know just how important it is to inspect all records and to reject insincere gerim.
A gerus for marriage is invalid, period. I saw with my own eyes how one Vashti in the guise of Ruth bought treyf food with her husband every time I saw her in the supermarket. They returned to the US, and they send their kids to a non-frum kindergarten. Tell me, please, what that gerus is worth.
She was the best of the bunch – other stories are not fit for this audience. Even non-religious Jews I knew would not do that in front of me, because they respect those who keep Yiddishkeit.
That being said, there is no reason we should respect the religious authority of the medine in any way, and it really can only decide “who is an Israeli citizen.” We must keep our own sifrei yochsin, and in one generation we will need them even to know who can get an aliya in shul (believe me, the non-kosher gerim will show up either to make trouble or for the Kiddush).