Wouldn't you then say "worst storm since record began?" Saying 1984 would be too ambiguous - people would probably think that there was a worse storm in 1984, but they wouldn't think that there was a worse storm "when records began"

Well, this is precisely the question under consideration! From the poll results so far, it seems to me as if only about 40% of people would naturally assume there was a worse storm in 1984.

Certainly saying "since records began" or better still "since records began in 1984" would be clearer; the question is, would it be so much clearer that you're entitled to infer that that's not what I meant or else I'd have said it?