Not sure if it was this specifically, but around that same time, Run-DMC would often instruct their audience during concerts to chant "We love Cool J!!" when asked specifically if they like/love Michael Jackson. I'm not sure that they were ever deliberately acting mean-spirited (the members including LL Cool J have long been fans; Darryl McDaniels even did one of the Thriller 25 podcasts), but some of the members seemingly let their fame get to their heads and grew huge egos. They believed, or wanted to believe, that they were bigger than Michael and said some things that could've been construed negatively by Michael...
Long before that, on the heels of Thriller in 1985, Run-DMC also released a song and music video titled "King of Rock" which in the title itself could be construed as a play on Michael's already crowned "King of Pop" label. In the song, they echo the lyrics, "They called us ill, we're gettin’ iller. There's no one chiller. It's not Michael Jackson and this is not 'Thriller'" In the music video for the song, they take a sequenced glove, drop it on the floor, and stomp on it. So yeah... They did a number of things over the years that could be seen as potentially annoying and negative towards Michael.
Of course, I doubt that anyone knows for sure exactly which factors contributed to the failed collaboration(s). I'm not so sure if it was specifically due to the construed negativity, in fact I think that Michael gave props to Run-DMC at some awards ceremony in the late 80s.
Here's the lyrics/pictures of Crack Kills draft:
Edit: Thanks for posting that quote from Quincy, Marni... I tend to agree with you too. Although Run-DMC may have said and done things that
could appear negatively targeted at Michael, I've never seen evidence that this is what caused the collaborations to fail.