Twilight Struggle: When are we allowed to do a Realignment Roll?
It sounds like you are reading "need not have any influence" as "must have no influence". Rather, it means "the acting player may take the action whether or not he/she has any influence in the target country."

When Ops points are used towards realignment, in a single "Realignment roll", both players roll a die and add their relevant modifiers. The winner removes the opponent's influence, if any, from the target country. So if you have no influence in the target country, you have nothing to lose, but less of a chance of affecting your opponent. You make one such "Realignment roll" per point spent, and you may target a different country with each roll (or the same country more than once).