The first is that instead of meditating as a young adolescent under a tree, the story is that he had a series of reflections about sickness, aging and death. Not that the two are exclusive. Perhaps the reflection led to meditation. Analayo points out that it's hard to believe he never saw these 4 sights in the legend where he goes out and sees these things for the first time. Perhaps instead he was preoccupied by these things for a long time.
Second is that his stepmother cried when he cut off his hair and put on robes. So he didn't sneak out in the night, or maybe he did, but everyone knew he was going during the day. So that tender image of him gazing on his wife and infant son, well, everyone knew he was going. His family was very much involved in his decision to leave, which does seem natural in those times.