Since when having a government fund your news organization is a good sign for legitimacy
PBS put out a lot of fantastic content. Sesame Street, Nova, Frontline, Nature, Reading Rainbow, News Hour...
Seems no better or worse than having privately funded news these days.
Well I would say that in this context legitimate means are they accepted by European society as "real journalists." The fact that the European government funds them does indicate that they aren't viewed by society as random crackpot bloggers.