In Ticket to Ride Europe a player may use a train station to use an opponent's route to complete a ticket. When a player does this, does the opponent's route count toward the player's longest route? The rules do not seem to explicitly address this issue.
No they don't. The rules explicitly state it twice.
In longest route scoring it states "Stations, and the opponents’ routes they may provide access to, do not count for the purpose of computing paths and claiming the longest one."
In rules for stations it states "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." So stations are only used to help complete tickets and no other use.