Thats very true. I raise show rabbits and rabbits in a breed are usually extensively linebred. In fact some breeds were started with just 2 animals! Rabbit breeders know that inbreeding and linebreeding are the fastest ways to express and fix good points in a breeding line- but are also the fastest ways to degrade a line too. Linebreeding is a very useful and important tool (in the right hands!!!) that is often ridiculed as "incest" or "dirty" or "wrong" by the general public.
I would not hesitate to purchase a horse that was line bred, but if I were to purchase a horse it better be a darn good one.
Can you post photos of the mare, and the naughty stallion in question? Maybe if we could actually SEE the animals it would be easier to judge what to do.
Spent a whole hour today laying in a pasture, waiting for a sparkling vampire to show up. Alas, I woke up and looked over, only to find a mound of horse crap. Sigh.