I don’t think he was in the car. I read an article somewhere that had this theory. They said that Kennedy and Mary Jo had been in the car together at one point but then later he got out of the car and she drove off. She was not familiar with the area and accidentally drove off the bridge. He didn’t report the accident because he was not aware of it until the next day.
I’m not sure why Kennedy would claim to be in the car if he really wasn’t. It doesn’t make a lot of sense, but it never made any sense that he was somehow able to get out of the car after it went off the bridge and she was not able to get out. Surely someone would have seen him in town soaking wet and would have asked him questions. But nothing like that happened.
So, after consulting with Markham and Gargan, Teddy ran the car off the Dyke Bridge and concocted the story about missing the turn in the dark, hours of disorientation, etc. Not very good, but the best that could be done on short notice. The point being, they all thought MJK was dead anyway, so they were just avoiding a legal complication by keeping Teddy away from the breathalyzer until his BAC returned to a legal level.
As it turned out, she wasn't dead, and if Teddy and company hadn't been so concerned about political office and damage control, the whole thing could have been cleared up that night, once MJK came around.
He wouldn't even have had to wear a neck brace.