This is just my theory, so take it with a grain of salt. Lochte, Feigen, Bentz and Conger all were celebrating at the French Club until sometime between 2:30 and 4 in the morning. They left the club, and according to their testimony hailed a cab at a nearby gas station. The gas station manager reportedly has no footage of them being there, though that has been contradicted by a story that came out today on ABC stating they got into a fight with a security guard at the station.
The ride from the gas station to the athlete's village looks to be about 15 miles, and I would assume could be covered in about 30 mins at that time of morning. They are shown on video arriving at the village at 6:56. Lets assume it took them 30 mins to hail a cab at that hour, then we add another 30 mins for the trip that would put them at the village around 5 at the latest. Now lets add in the robbery, that could not have lasted more than 5-10 mins at the outside. That places them in the village at 5:15, and no later. What happened to 90 + minutes?
The story broke in the following manner, Lochte spoke with his mom and told her about the robbery. Lochte's girlfriend is supposedly staying with his mom. My guess is that the late arrival at the village meant a late arrival to meet up with his mom and girlfriend that morning. To explain the delay Lochte blurted out the story that he was robbed, and fabricated the details to his mom to make it believable. Lochte did not report this story to anyone else other than his mother. Later that day in an interview with Fox Sports his mother repeated the story about the robbery and the rest is history. In order to cover, what my guess is some male fun from 4-6:30 in the morning, Lochte when questioned about the story corroborated it and asked his teammates to cover as well not suspecting that Brazil being very sensitive to their image would immediately verify what went on.
That is my theory, take it or leave it.