I think it gets interpreted differnetly.
While your version and mine of Machado's slide are similar, I think Pedroia simply wanted to stop the headhunting, especially if he felt Machado thought he put Barnes up to it. If that was the case, that makes Pedroia the target for Baltimore pitchers. A lot of fans might not like it, but stopping the headhunting is a good thing.
Machado's slide wasn't that different - and actually less egregious - than many other slides he went into 2B with. We've all seen him take out slide into Pedroia the previous season while missing the bag but able to grab it with his passing arm (which was legal at the time).
Certainly he wanted to collide with Pedroia; it's part of breaking up the double play. I don't think the spikes were necessarily intentional, and I do think he tried to help Pedroia up because, as a former shortstop, he knows what it's like to be on that side of the play as well.
As for Bogaerts, he could have been referring to anything. There are so many incidents in clubhouses and so many conflicting personalities. It's a scene of 25 guys with massive egos who don't all like each other and never will, and a coaching staff trying to keep all that in check. Tension could come from a multitude of places. The worst tension usually comes from a consistent source, not a singular event. I'd think Bogaerts was referring to some other far more drastic change
It's actually even hard for me to believe the team was even united against Pedroia after that comment. Much like on this board, the players themselves probably took it differently. Maybe a few were offended and maybe a bunch of others agreed with Pedroia. But this type of reaction can happen with any comment, and is probably more commonplace than most of use realize. I would be VERY surprised if Pedroia's comment had that much of a lingering effect, especially since the Sox pitchers continued to throw at Machado a couple more times that year...
This strikes me, much like chicken and beer, as another of those incidents that was taken far more seriously by fans outside the locker room than by those in it...