An account of the Capa D-Day coverage - which is part of Photo lore by now - can be read here
Actually, Capa landed with the first wave, not the second, on Omaha Beach.
His editor John G. Morris is still very much alive and well in Paris.
Another D-Day photo lore is the story of AP photographer Marty Lederhandler who landed on Utah Beach on June 6. Like many photographers, he had been provided with two caged pigeons to fly his films back to England. The photographers and their pigeons had been stationed for two days inside boats before the landing because of bad weather.
After landing in Normandy, Lederhandler released his pigeons and saw one of them - by now disoriented - flutter into the ski to turn east instead of west!
The pigeon flew into German lines, the film was captured and Lederhandler's photos were published - with full credit - on German newspapers.