It is claimed here from minute 50 onwards. Also he claims that he drank 2l of the water and that he ate some uranium.
If the claims of Mr. Winsor are true that he worked as a safety manager in a nuclear plant, it is highly unlikely that he was actually able to accomplish anything that would have legitimately given him a lethal dose of radiation.
Swimming in the pools is actually a fairly standard practice among workers servicing spent fuel pools. Divers are used to inspect the submerged fuel rods for damage, and are protected from radiation by the water itself. As it turns out, water is actually a very good radioactive shield, and divers are safe as long as they don't get too close.
On August 31st, 2010, a diver servicing the Leibstadt nuclear reactor accidentally handled a radioactive piece of tubing on the floor of the pool. The diver was very deep in the pool and did not hear his radiation alarm go off upon picking up the object and putting it in a transport basket. The worker received a large dose to his hand, but was otherwise OK. As can be seen from the report, there was no loss of life or serious injury from the incident, and it appears that this was a case where the diver had picked up a piece of debris from one of the fuel rods and moved it with his hand.
This report was put out in 1977 regarding the protocols and safety of storage of spent fuel rods within pools. The report itself is very long, but after skimming through it for about a half an hour there are a couple of things to point out.
The average pool from the limited pictures and data in the report indicate that these pools are typically at least 28 feet deep, requiring the use of diving equipment in order to reach the bottom.
The amount of radiation in the water is typically measured in the 10s to 100s of nanoCuries/mL of water. Thanks to this handy document from the Army Corp of Engineers, nanoCuries are about the same amount of radiation emitted by consumer products. Two liters of water from one of these pools would be emitting approximately 200 microCuries. While this is well above what is allowed to be sold in stores, this is approximately 1/5th amount of radiation given off as from a brain or liver scan.
In terms of eating uranium, chances are that if he did, in fact eat Uranium, he did not eat enough of it to cause any lasting impact on his body. Ironically, the primary danger of eating uranium is not radioactivity, it is toxicity. According to the CDC...
Natural and depleted uranium have the identical chemical effect on your body.
The health effects of natural and depleted uranium are due to chemical effects and not to radiation.
A cursory reading of the CDC report on uranium says, simply, the toxicity will kill you before the radiation does. So any possible consumption of uranium on the part of Mr. Winsor must have natually been low enough that he did not poison himself chemically, as evidenced by the fact that he was still alive to record the video.
While this is not as scientific as some of the other sources, Randall Munroe of XKCD posted a What If? article a few years ago regarding swimming in a radioactive fuel pool. Some of my initial research came from references in this article, but his conclusions are similar to mine.