Can stations be used to traverse empty routes in Ticket to Ride Europe?
I don't actually see any ambiguity here. You've quoted the rule saying a Station allows you to use someone else's route. I don't see how that could imply that a Station can complete a route that hasn't yet been filled in by anyone.

The reason you are allowed to place Stations on any city, including currently unlinked cities, is to allow you to place a Station strategically, before anyone else. This is important, because only one player can control a Station in any given city. If you suspect that in the late game you will need a Station in a city, or you would like to block other players from placing a Station, then this could be a smart move.

The purpose of Stations is to give you the possibility of still completing routes, albeit at some cost (since you don't get your four points at the end for the unused Station). As you point out, if you could use them to effectively 'jump' the last leg of a route, then that would change the entire dynamic, and would indeed make Stations much more powerful.

So based on the rules, and the intended use of Stations, I'm quite confident that completing empty routes using Stations is not intended, or legal. Someone that's played the online version of the game could confirm this, though.