Falun Gong media is not transparent about its affiliation (法轮功媒体对其隶属关系不透明)

Agreed, and it is a point that hurts more than helps their cause.

This is very clearly put as well at "Front groups" of the Orange Papers (橙色文件).

But the media is not legally obliged to state their affiliation.

And if that were the case, then we should force all newspapers to start taking polls of how many employees follow which religion and support which political party, and then put that in their print.