Sussex Murder Mystery Puzzle?

(This is in the Math section because it takes some math to solve this one)

Detective Mathieu has less than a day left to decide to arraign which of the two brothers, Alex and Brian, now in detention since their arrest following the murder of their father, found dead with one 9mm bullet in his heart, hidden in the bushes of Sussex Park. He is sharing a coffee with their chauffeur, Craig, after hearing from him again that he drove the same route every workday to pick up the sons at the Essex Train Station, at 5:00 pm when the train arrives, to take them home. He said he regularly uses cruise control to maintain constant speed at the low posted speed limit, and that he times himself so well that he consistently shows up at the train station at 5:00 pm, and returns to the estate home 15 minutes before the 6:00 pm local news, which he likes to watch.

The motive for the murder is clear–it was announced that their father was planning on cutting them out of his will, leaving it all to his new 2nd wife. The confirmed 9mm murder pistol was fortuitously later found in the lake. It was common knowledge that the father regularly ran laps around the lake in Sussex Park in the afternoon.

Alex said that after an angry argument with Brian, he left on an earlier train, arriving at Essex station at 4:00 pm, and then decided to walk home, expecting to see Craig sooner or later. He said he stopped for coffee in town on the way, but nobody could be found to recall seeing him having coffee. Surveillance cameras at Essex station confirm his leaving on foot up the road at 4:00 pm. Brian said he arrived at 5:00 pm, also decided to walk home, but then realized that Craig was probably already heading home with Alex, so he called him to turn around and pick him up. Phone records confirm this call at 5:08 pm, and surveillance cameras at Essex station confirm his leaving on foot up the road at 5:00 pm. Both denied taking the short cut through the park from E1 to E2.

In the brief time Detective Mathieu was with the sons together, he heard Brian say, “Alex was telling me that he was going knock off dad!”, to which Alex angrily replied, “I was joking, Brian, but I didn’t ever think you’d actually do that!”

Craig said he remembers picking up the sons both times before reaching the bend around Sussex Park, but doesn’t particularly remember where along the road. A surveillance camera at one of the industrial buildings shows his car travelling away from the town, but because of the tinted windows of his limousine, it couldn’t be ascertained if there was one or two passengers, and the time of the video couldn’t be accurately ascertained either, although it was obviously afternoon.

Detective Mathieu rubbed his brow, trying to make sense out of the timeline, reviewing a sketch he had made (see link). The body was found at X, the gun at Y. The industrial building surveillance camera is at Z. The only two ways to enter or exit Sussex Park is at E1 and E2. The sketch is drawn to scale from published maps. Craig picked up his coffee, and said sympathetically, “You know, I didn’t even know anything about this until the police showed up last night. When I got home, I had just missed the first minute of the news program that broke the news of the body found at Sussex Park.”

Mathieu’s eyes suddenly lit up, as he rapidly understood the implications of what Harry just said with savant-like speed. “Oh!”, he said, standing up and pacing around, “Oh,… well, it’s a very good thing that you remembered that, Craig. That means neither of the sons is likely to have murdered the father!”

Why did Detective Mathieu decide that? BA goes to the most convincing explanation.

http://i254.photobucket.com/albums/hh120/Scythian1950/SussexPark.jpg
Dr D (or should I say Detective D?), how does the location of the found gun help support Mathieu’s decision?
Detective D, you’re quite right in that Mathieu doesn’t yet have enough information to know who was the killer, but at least he knows the neither of the sons are likely to be.
Detective Mathieu also realized that if either Alex or Brian killed the father at X, and decided to backtrack to entrance E1, much more likely the gun would have been dumped in the lake near E1, not E2.