Thus, a tritium-infected fish might be damaged, but would not be radioactive if consumed by a human. Correct?
It wouldn’t even be damaged.
The beta from tritium is so low energy that it causes less damage than sunlight. Of course it’s always there. It comes and goes as the fish exchanges water with the environment, i.e. biological half-life. If the tritiated water is dilute enough, no problem.
Back in the old days, treated reactor coolant was routinely dumped in the ocean by the navy outside the 10 mile limit.
That has not happened for many decades.