I'll skip the "seems plausible" conjecture, and focus on the professor who says:
The concern is that not any one person eating one tuna is gonna have a problem, but that over large numbers of people, the small increase in radiation will produce a small increase in cancer risks.
If we look at the Linear No-Threshold model, what the professor says is absolutely true. There are two other main models, the Threshold model that says up to a certain level radiation is benign, and the Radiation Hormesis model that says up to a certain level radiation is actually beneficial. Thus, the LNT is obviously the more conservative of the three. As far as I am aware, the other two models are more favoured scientifically and LNT is just a compromise. Note, however, that UNSCEAR says this:
Due to the great uncertainties in risk estimates at very low doses, UNSCEAR does not recommend multiplying very low doses by large numbers of individuals to estimate numbers of radiation-induced health effects within a population exposed to incremental doses at levels equivalent to or lower than natural background levels.
This is what the professor is doing. Looking at data from east Pacific tuna presented here, we see:
In bluefin tuna caught off San Diego, the total radioactive cesium levels were 10 becquerels, only three percent above radiation levels from naturally occurring potassium-40, and far below safe-consumption levels set by the United States and Japanese governments.
I shall assume they mean 10 Bq/kg.
A single banana, by comparison, has 15 becquerels of potassium-40, or, given a 150 gramme banana, 100 Bq/kg. Therefore we are looking at less than a tenth of the effect (or indeed 40% of the 25 Bq/kg from the C14 in the sugars in a banana). However, I have seen it argued that (a) the body has evolved to handle natural radiation (now that would be a good question for here!) and (b) it bio-accumulates, unlike K40 and C14.
Therefore, I conclude that Professor Daniel Hirsch (ad hom: a politics lecturer and anti-nuclear campaigner) is correct in what he says, but he goes against the advice of UNSCEAR to produce his conclusion.