Or simple contraposition :-PPlease correct me if I am wrong, but if the relevant part of the article is "I do not have insurance, so it is important that I maintain my health", then the contraposition would be "It is not important that I maintain my health, so it follows that I have insurance." What you are suggesting as the contraposition is "I have insurance, so it is not important that I maintain my health", which is the inverse of the statement (and equivalent to the converse "If it is important that I maintain my health, then I do not have insurance."