OK, here goes by memory without references

:
At 11:15 PM Ted and Mary Jo leave "The Boiler Room", the notorious cottage known for liaisons between the Kennedy Men and their girls. They are both heavily intoxicated, and are seen by all there as leaving at that time.
At 12:30 AM, a sheriff's deputy notices a car (matching the color and general shape and size of Kennedy's car, though he doesn't know that) sitting in a local lovers lane on the island. As he approaches the car, its engine suddenly roars to life and the vehicle tears off, leaving the deputy in a cloud of dirt and dust.
At This Moment, Ted & Mary Jo do not know the following facts:
1] The deputy saw no faces
2] The deputy did not get the license plate #, state of origin, make, or model of Ted's car
3] The deputy has no access to any form of transportation
4] The deputy has no access to any form of communication
5] The deputy is completely alone
6] Ted and Mary Jo have just made a clean getaway
At This Moment, the heavily intoxicated Ted & Mary Jo have to assume the worst:
1] The deputy recognized Ted
2] The deputy saw him in a compromising situation with a woman not his wife
3] The deputy got the license plate #, make, and model of Ted's car
4] The deputy is already racing to his vehicle
5] The deputy is already calling in for police backup
6] The deputy is now in Hot Pursuit

7] Police backup are even now crossing Chappaquiddick Bridge cutting off escape
8] The police are all Nixon Republicans
So, what to do? Cook up a scenario!
Ted tells Mary Jo to take the car and travel by herself to go home. If she's stopped, she can just say she was driving home by herself. The people back at the cottage will back them up, and the report by the deputy can be dismissed on the grounds that he was merely mistaken in the darkness of the night.
Mary Jo, with a blood alcohol level that's probably past .3, driving at night in an unfamiliar vehicle on a bridge with no lights or guardrails slips off the bridge as the drivers' side forward wheel going first. The car tips over at a 90 degree angle, causing a "bellyflop" impact on the drivers side of the car, transferring the shock of said impact to the un-seatbelted driver (nobody wore seatbelts in those days

). Knocked unconscious, Mary Jo wakes up as the cold water floods in, and she instinctively goes to the air pocket forming at the rear seat window. This air quickly fouls with CO2, and its not certain whether it is this or exposure from the water that causes her to lose consciousness again, and drown. There's no indiction that she tried to open the windows or the doors, but its not uncommon in these circumstances for the force of impact to jam both windows and doors.
Ted has been walking about the island, thinking to let the police speak to Mary Jo while he is on his "late night constitutional". By the time he crosses the bridge himself, Mary Jo is already dead, and the car is
almost completely submerged, and invisible at night.
He then goes to the motel right at the end of the bridge and checks in. He then proceeds to get chatty with the night clerk, who is flattered that the famous Senator Ted Kennedy would choose to spend so much time with him. Ted spends much of the night traveling back and forth from his motel room and the front desk (establishing his whereabouts) until finally by 3AM (figuring Mary Jo is home and in bed herself by this time) he goes to bed for the night.
At 7:30 AM he gets up and goes outside. Pandemonium! Emergency vehicles everywhere! And who is the first person to see him? His Chief-of-Staff! NOW What!? Simple: Cook up Scenario 2.0
Problem: Oh what a tangled web we weave when first we practice to deceive
That is why he limited his fairy tale press conference to local media
That is why he had to cook up a ridiculous tale that FIT HIS KNOWN MOVEMENTS FOR THAT NIGHT
The press would NOT question his dry clothes. They would NOT question his movements at the motel. His only unanswerable problem was the sheriff's deputy, whose recorded timing in his notebook of the event at the lovers lane could not in these circumstances be elided. So...the deputy was a liar.
The deputy is quoted as saying: "Look, you can either believe him, or you can believe me." Apparently, the voters believed him. They elected him Sheriff.



After the 10th anniversary of Chappaquiddick, the local Coroner who had "lost" much of the files on Mary Jo Kopechne's autopsy asked Ted's CoS to secure a political patronage job for the coroner's son. When Ted's CoS refused, the coroner is reported to have said: "Oh really? Then I think I just remembered where I left some old files of mine!"

So at the time that Ted was getting ready to challenge Carter for the nomination, "leaks" came out showing that Mary Jo was still alive and conscious for some time after the car went into the water, putting the complete lie to Kennedy's fairy tale about "swimming to the car but not being able to save her".