This is an interesting issue. You've got a private event organizer, a public space, private citizens competing in the private event on public space, a participate of the private event publishing images of the private event and of the private citizens in the private event, and an written agreement between the private event and participates of the event. There is also a commercial use issue with the publication of the material to the internet.
This probably falls under the developing legal category of "street style photography."
For a host of reasons, not just monetary, the BAA probably doesn't want a bunch of unregulated street style photography of the event posted on the internet. The race enters into agreements with media outlets and photographs, who generally abide by a set of commercial standards. Private citizens often do not.
At a minimum, I suspect courts would find that the BAA may ban the participant from running future Boston Marathons for explicitly breaching his agreement with the BAA. I also suspect that it can obtain an injunction requiring the content be removed from the internet.