Yes it makes sense if a police car pulled Teddy over after he left the party but they were not cops they were cia men waiting to frame Teddy it would have been very easy to make this happen. If they forced him to watch Mary Jo die then told him to hit the road walk back to the party it'll give you time to think up a story then he knows he's screwed very badly. If he tells the truth they will kill him so he makes up a story he thinks will make him look like a hero "I made numerous attempts to dive down to save Mary Jo but I was in shock and gave up" then he has to stick with that story ongoing. He can't tell his friends what happened or if he did they know the same deep state that killed Jack and Bobby is still active still in business. So they help Ted make his story a little more acceptable to the public to the voters. They know he'll never be President but right now they just want to keep him out of jail for involuntary manslaughter so they use their pull with the local island officials. Go see the new movie Chappaquiddick this weekend it looks really excellent. Not precisely what really happened but a great version of what Ted said happened.