I hope I'm not repeating myself - sometimes it feels like I'm going round in circles and it buzzes in my head to the point where I can't remember what's made it as far as my keyboard.
From the books and documentaries what I get is that the music business of the 1970s was a tough place to be and that negotiation techniques and contracts were not what would be considered fair or good practice these days. There are stories of bands who had hits, worked hard but found themselves in debt because the way their contracts were worded. Managers ripping off bands, even suicides. Tom Petty fought to win back his publishing which he'd signed over without realising early in his career. Pete Townsend was pretty broke in the late 1980s before the 1989 tour made him a millionaire. Geffen and Azoff seem to have done well by their clients even if they did even better for themselves. For example, Geffen only took half the publishing.
It was a dirty business and the managers fought dirty for their clients. Just because there was a contract in place, didn't mean it couldn't be changed retrospectively. Geffen was known as a shark, and Azoff was known for being very unpleasant to deal with because of how he would scream at people. Azoff used the carrot of a new album and the stick of it being delayed in order to change how much the Eagles received for the earlier albums and the record company agreed because they needed that album to deliver the numbers their shareholders were expecting. And they were making so much money out of the band that they could afford to pay more.
That was the environment in which the members of the band learned about negotiations. Everyone was out to screw them so they just needed someone ruthless on their side. Contracts could be renegotiated and they used their power to get what they wanted.
Where I'm going with this is that I think it helps explain why Frey/Henley/Azoff felt they were able to renegotiate contracts in 1994 and why they might have thought it reasonable to be quite assertive about it.
On a slightly different tack, all the band members were poker players, so perhaps part of it was about knowing the strength of their hands and bluffing or being able to walk away.