That, and alligators don't really see people as food, unless you are a small child playing near the edge of the water at dusk. They can be defensive of their personal space and breeding territory, but they'd much rather be 10ft away from you than attacking you.
Source: Spent a week kayaking in a burning swamp absolutely filled with alligators. They just want to sit in the sun and be left the fuck alone.
Also they're generally chill. I grew up in South Florida and have encountered more than my fair share while canoeing, and outside of breeding season you can walk right up to them and give them a slap and tickle and they couldn't be fucked to give you any grief.