Question: “The German TV broadcasted that anyone who enters Greece after the 15th of March will be only eligible for asylum in Greece but all the ones who entered Greece before this date, especially the vulnerable cases, will be accepted for asylum in another EU country.”
Answer: The only legal ways to move from Greece to another European country are the relocation program or through family reunification, if eligible.
If you entered Greece after March 20th, 2016, you are not able to apply for relocation. This is a program that concerns the transfer of asylum seekers from Greece and Italy to another EU country, if eligible.
However, you might be able to have your asylum applications examined in another European country, if you are eligible for family reunification. But several conditions apply for family reunification.
A general overview of the rules is available here.