> Water cannot be radioactive
To start, seawater has more things than water. Both Hydrogen and Oxygen have isotopes that can decay and emit radioactivity, so yes, water can definitely be radioactive, by definition. For a relatively short time because is not plutonium of course, but it can be.
And, unlike Plutonium, the problem is that life beings are mostly made of water and we didn't coevolved with a such rare element as tritium is in nature. Water is freely allowed to enter and travel and has granted access to every part of the human body. We trade a big danger for other, but this does not mean that radioactive water can't harm us.