The argument treats the gap between fish-oil users and non-users as proof that the supplement lowers blood pressure, but the users are self-selected, so they could simply be people who already keep their blood pressure down some other way. The stem even notes that many people start taking fish oil after a doctor warns them about rising blood pressure, which if anything should bias users toward higher, not lower, readings, so the lower readings need an explanation.
(E) is the assumption the argument depends on. If you negate it, so that fish-oil users already tended to follow low-salt diets and exercise habits before they started taking the supplement, then their lower readings trace to those habits, and fish oil is not shown to have done anything. Because the conclusion collapses when this is false, the argument depends on it being true.
(A) is the closest wrong choice: it also blocks one possible confound among users, a second supplement such as magnesium that is already known to lower blood pressure. But ruling out only magnesium leaves every other health habit that could explain the gap untouched, so even if the argument does not depend on magnesium specifically, the conclusion does not automatically fail; negating (A) does not collapse the argument the way negating (E) does.
(B) concerns whether the dose is large enough to matter in principle, which does not address whether self-selection, rather than the pill, produced the gap. (C) concerns whether advised patients actually complied, which speaks to who ends up in the fish-oil group, not to what caused their readings. (D) concerns whether the blood-pressure equipment is calibrated consistently, which rules out measurement error, not the possibility that the two groups differed for reasons other than the supplement. Only (E) closes the gap between correlation and causation that the argument needs closed.