I think Reptisaurus's recollection is correct (aside from the extra details that shaxper added). Yes, Byrne was the guy early on who fought to keep Wolverine in the series. But it's not that Byrne wanted him nicer. Rather, Claremont though Wolverine was uninteresting until he developed more nuance.

Byrne is the more black-and-white guy and Claremont is the shades of gray guy. Byrne is more likely to think see less nuance in violence. I'm 99.9% sure that the idea about disemboweling Kitty at the breakfast table was Byrne's idea. It's important to note that it was a joke rather than something he ever intended to put in the series. But Byrne's point is that if Wolverine really has that violent pathology, killing an innocent teammate before he's realizes what he's done is something that could actually happen. Claremont is the guy who sees complexity in violence, but he often takes it to idiotic lengths. Claremont has said he likes heroes who kill, and he tries to excuse it with a cloak of nobility. Claremont wrote Uncanny #219 where Storm suggests the X-Men kill Havok simply because he stumbled upon the X-Men's plan to fake their deaths. In a sane world, that would result in the rest of the X-Men voting unanimously to ban Storm from the team for life for being a psychopath. But for Claremont it's "sophisticated" to consider the tough choice of killing an innocent person on some flimsy pretext. And let's not forget Wolverine and Rachel circa #208-209.

So:
Byrne = killing innocent people is a crazy impulse
Claremont = it's deep and mature to pretend killing innocent people could be sort of moral

The turning Wolverine bad thing was supposed to happen in the 200s, I think culminating around #300 (if Claremont had stayed with title). It was premised on the notion that Wolverine is bad. He was going to be presumed dead, and then brainwashed or possessed by the Hand or the Shadow King or someone. So it was really part of Claremont's pattern to build more stories around one of his favorites.