I haven't seen this in print in any speculations but a likely guess is that Ted's pants were off when they sped away from the guy approaching their car. Hence, he was half naked at the time of the plunge off the bridge into the water. Panicked and half naked, after a brief search to try to get her out of the car, he ran back to the cottage to get a pair of pants. By the time he returned with the handlers and cronies (and none of those drunk liberal dorks could figure out how to get her out of the car), it was too late. Leaving open the likelihood, she died because they were afraid to report an accident incriminating Ted in drunk driving and cheesy adultery.
The absurd changes in his story reflect his reluctance to admit he was half naked at the time of the accident which ocurred after they interrupted engaged in hanky panky.
Nothing, of course, would surprise me with the Kennedy Klan. They all seemed to have liked keeping their britches down around their knees. Your speculation might not be so far off (at least not as far off as Teddie's britches!).