You're maybe thinking about this in a way that's not helping you to understand the system and why it works the way it does. It's very clear when you think of a specific case.

Say you want to make a recording of "Valerie" by the Zutons. You need permission (a license) from the songwriters (the Zutons presumably) to do this. You usually get this permission by paying a fee. Having done that, you can do your recording. Whenever that recording is played (or used) you will get a performance royalty and they will get a songwriting royalty.

Say you want to use a cover of "Valerie" by the Zutons in your film or whatever. Say the Mark Ronson version featuring Amy Winehouse. You need permission (a license) from the person who produced that version (Mark Ronson or his company) and will need to pay them a fee, some of which goes to the songwriter as part of their deal with Mark Ronson which gave him the license to produce his cover in the first place.

The Zutons don't have the right to sell you a license to Mark Ronson's version so if that's the version you want you have to negotiate with him. Likewise he doesn't have the right to sell you a license like the license he has (ie a license to do a recording/performance) so if you want that you have to negotiate with them.

OK it seems exactly what I thought and described, and the opposite of what the parent poster described. The parent poster said that if you want to use the cover of the song you need to negotiate with both the people who did the cover and the original rights owner.

The closest I could get to a situation like that would be if I told Band B do a cover of Song A for my movie and I paid the licensing costs as part of my deal with Band B, but still not the same as the parent poster's description.