That being said, even with this explanation in full view, considering Picard commanded the 7th Fleet;
When was that stated? Plus he was not even a admiral? So he could only be a aid like Sisko was.
It doesn't need to be stated, its fact. This is simply a nature of the beast. You should consider reading up on such things here:
Knowing about the business makes it fairly easy to see how and why things are done without being spoon fed explanations of why decisions are made. We don't need to have full details about the cast members contracts to know what is typical for an SGA negotiated contract.
This is generally why you don't see too terribly many crossovers in live action series and when you see them in animations there's often some sort of wonky disconnect (IE when the Fantastic Four crossed into the 90s Spider Man series, they wore different uniforms and had different voice actors even though they were essentially within the same design).
Sometimes unions help a lot, sometimes unions make things endlessly difficult =(.