Maybe, but I tend to think that some of the crosstown stuff is really just driven by the fans less-so-than-teams. I think if the Cubs had offered a similar package but done so a week ago, before the Red Sox went there, Crochet would be a Cub. I doubt the White Sox would have turned that equivalent package down and thought "man, oh, man, that's a good offer but because Dave Kaplan might say something I better ask for more or just trade him for less to another team!"
But in the end, I don't blame him for not sending that package. The Cubs don't have three other universal top-10 guys like the Sox do right now, so losing a Shaw hurts a bit more - especially if you're thinking he's going to take over for Parades in a Tucker trade.
I like Crochet a bunch! And I think for the Sox it made sense - both Sox.