I believe the chelonian in the video was a gopher tortoise. When looking for information on the swimming abilities of gopher tortoises in particular I found several press releases telling people that gopher tortoises cannot swim and not to put them in water. Apparently there’s been a pretty serious problem with people mistaking baby (or even adult) gopher tortoises for sea turtles and throwing them into the ocean.
I doubt that gopher tortoises can’t swim at all. The concern is more that they can’t swim well enough to avoid drowning especially as hatchlings or in deep/rough water. There are even semi-aquatic turtle species that are known to drown sometimes when placed in inappropriate conditions; they can certainly swim but they aren’t strong swimmers.
Aquatic turtles don’t have to paddle constantly to stay above water; they can actually regulate their buoyancy (it’s a somewhat complicated balancing act between the amount of air and water in their body). Most tortoise species are able to float pretty well in water probably via similar mechanisms. In fact an Aldabra tortoise once floated 700 km across the Indian Ocean from its island home to mainland Africa (and survived the trip!).
However if a tortoise had evacuated all the air from its lungs and was dropped into deep water it could absolutely drown. Whether the tortoise from the famous video survived or not is unknown (as far as I know) and I honestly can’t say for sure what would have happened. What I will say is that she should not have dropped the tortoise from that height; even aquatic turtles should be placed on the shore to enter the water at their own pace. And turtles in general should not be removed from the place where they were found unless they are in immediate danger.
Unfortunately, this has been an on going issue in Florida. Well-meaning people put gopher tortoises in the water, thinking they are sea turtles in need of rescue! Gopher tortoises can be found in the dunes near the beach and will make a trip to the surf to remove ectoparasites like ticks.
The feet are an excellent way to tell the difference in the two animals. Tortoises have claws for digging burrows as opposed to flipper-like appendages. The carapace of a sea turtle is also flatter than a gopher tortoise carapace. This quick identification can be done without touching the animal. Turtles are best left alone unless they are in immediate danger.
If you find an animal on the road that you can safely move, move it, especially if it’s small or slow.
If you find an animal on the road and aren’t certain whether it’s a turtle or a tortoise, put it next to water, it’ll go in if it wants to.