I've always wondered whether the 'bobcat misunderstanding' is actually more about timing rather than what Barry had done to the bobcat. Maybe LE confronted him with the story of SM abruptly ending communication with her friend at 12:30 on Saturday, and he told them he was in town getting the bobcat repaired at that time. But his phone data showed him at home? Or something like that.
His actual quote to LS was
"It was only because I didn’t know the time that I did something, a mechanical thing, to my bobcat..." So maybe the bobcat isn't involved because it was used to hide her body, but because he tried to use the repair job that JP talks about as another alibi once LE started focusing in on Saturday.
Or maybe both, if he killed her during that 11-1 window and then immediately went to get mechanical work done on the bobcat, he might have had later plans for it.