Ms Nyad, 64, said she swam without holding on to any boats or people accompanying her. "I swam. We made it, in squeaky-clean, ethical fashion," she said.
Her critics are suspicious about long stretches of the 53-hour swim were Ms Nyad appeared to have either picked up incredible speed or to have gone without food or drink.
Since Ms Nyad finished her swim on September 2, long-distance swimmers have been debating it on social media and in online forums.
Her speed, at some points more than doubling, has drawn particular scrutiny. Her team has attributed this to the fast-moving Gulf Stream flowing in her favour.
Ms Nyad's navigator John Bartlett said her fastest speed averaged about 3.97mph over a 5.5-hour period over about 19 miles, crossing the strongest parts of the Gulf Stream, which was flowing at a favourable angle.
Ms Nyad attempted the swim from Cuba to Florida four times before finally completing the journey,