That headline is the conclusion of a Cochrane systematic review of the evidence. As you read the summary below, be aware that the main omega-3 fatty acids are alpha-lenolinic acid (ALA), docosahexaenoic acid (DHA), and eicosapentaenoic acid (EPA).
From Cochrane Library:
Increasing EPA and DHA has little or no effect on all‐cause deaths and cardiovascular events (high‐quality evidence) and probably makes little or no difference to cardiovascular death, coronary deaths or events, stroke, or heart irregularities (moderate‐quality evidence, coronary events are illnesses of the arteries which supply the heart). EPA and DHA slightly reduce serum triglycerides and raise HDL (high‐quality evidence).
Eating more ALA (for example, by increasing walnuts or enriched margarine) probably makes little or no difference to all‐cause or cardiovascular deaths or coronary events but probably slightly reduce cardiovascular events, coronary mortality and heart irregularities (moderate/low‐quality evidence). Effects of ALA on stroke are unclear as the evidence was of very low quality.
There is evidence that taking omega‐3 capsules does not reduce heart disease, stroke or death. There is little evidence of effects of eating fish. Although EPA and DHA reduce triglycerides, supplementary omega‐3 fats are probably not useful for preventing or treating heart and circulatory diseases. However, increasing plant‐based ALA may be slightly protective for some heart and circulatory diseases.