Royalties and access to songs have nothing to do with this. Scott is entitled to songwriters royalties regardless. The same goes for the songs, there is no legal mechanism to prevent him, or anybody else from performing STP songs. He doesn't need permission, and no lawsuit can take away his royalties, except one that proves he didn't really write them, which obviously he did.
This was all about the brand, who controls it, who can use it.
My personal total guess is that they asked for a crazy amount in their lawsuit to scare him into ducking out of his 1/4 share of the brand. He took a small settlement and agreed to leave rather than risk continuing the lawsuit and losing, which he may well have done. The band never really wanted a massive payout from him, not least because he couldn't pay it anyway, they just wanted the brand and they clearly got it.
What is really interesting now is that with Scott out of the STP partnership, if they wanted to get back together they'd have to either hire him, or make a new contract. It makes it more difficult anyway, as before they could just reconvene under their original agreement, now that doesn't exist.