The argument treats the gap between users and non-users as the supplement's effect, but the users are self-selected and could simply be people who already manage blood pressure well by other means, and the stem even notes a selection effect (people start fish oil after a doctor's warning) that, if anything, should bias users toward higher readings, making the observed lower readings demand an explanation.
(E) is the load-bearing assumption: negate it and the fish-oil group was already eating low-salt and exercising more, so their lower readings trace to those habits and the supplement is not shown to do anything.
The same-axis near-miss is (A), which also guards against a confounding cause among users, but it forecloses only one specific co-taken supplement; it leaves every other healthy-habit explanation untouched, so its negation does not collapse the conclusion the way (E)'s does, (A) is too narrow to be a depended-on (necessary) assumption. (B) addresses dose in principle, (C) addresses compliance with advice, and (D) addresses measurement calibration. Only (E) closes the correlation-to-causation gap the causal claim requires.