I don't find train station irritating. It's a very clear expression, like bus station, fire station, ticket station, police station.
As for riding, well the same applies. Horse riding defines the type of riding. One can ride a donkey, ride in tandem, take a bus ride, ride a scooter etc.
When someone said they'd just been fencing, as happened several weeks ago, I knew it meant 'fencing in', as in making an enclosure, as he's a farmer. So using sword fencing is useful in defining the type of fencing.
I could go on.....
I guess pickiness works both ways.