It's not a rephrasing, it actually isn't even the same rule. It is two different rules with similar phrasing. One is a prohibition, the other a mandate. You cannot rephrase a prohibition into a mandate or vice-versa. There is no trick of semantics that can turn one into the other.

Your "better rule" though, it is a third rule and not a very good one. It counts on you knowing what they would not have you do unto them.