The Proper use of Stations in Ticket to Ride Europe
There's no concept of direction of travel in Ticket to Ride.


  If, by the end of the game, a player has created a continuous path of his color plastic trains between the two cities named on a Destination Ticket he holds, he scores the additional points indicated by the Point Value on the Ticket. If he has failed to complete a continuous path between those cities, he deducts the Point Value on the Ticket from his total score.


A path between cities must be created. Nothing about traveling from one of the cities to the other city.

As such, the Brest-Madrid path exists because it did use the same route into Paris as the Frankfurt-Madrid path, the Pamplona-Paris route.

Ticket to Ride is a simple game with straightforward rules. It's obvious to me that the purpose of the second rule you quoted is to prevent the station from being used to borrow two different routes. In fact, this is stated explicitly earlier in the rules (quoted below). It's a botched attempt to clarify this rule (which was already plenty clear).


  A Train Station allows its owner to use one, and only one, of the routes belonging to
  another player, into (or out of) that city to help him connect the cities on his
  Destination Tickets.


This means your group is clearly wrong when they believe that several routes going out of a city could be borrowed.

My proposed rewording of the second rule you quoted is the following:


  Only one route is ever chosen per station. This means that a player can't have a station grant him the use of two routes for two different tickets, but any number of tickets can use the chosen route. The Train Station owner does not need to decide which route he will use until the end of the game.