Our horses are on a 40 acre pasture, so I cannot do the run them down thing, though I know what you are talking about.
So, since they are in a herd and where goes one, go the others, I put some tasty hay on the ground and let the other horses come up and feed. I do not allow my target horse to approach the hay. I drive him off. He runs way off and circle to the other side of the hay pile and I drive him off. I do this until when I drive him off, he changes his mind and turns back toward me. I then try to approach to halter him. HOrse know the difference between when you are approaching to drive and when you want them to stand there and be haltered. If he doesnt' let me approach then I drive. What keeps him within the area where I can do this (instead of out on the 40 acres) is the yummy pile of hay everyone else gets to eat.
Once he is caught, I may give him some treats or take him over and give him his own handful of hay on the ground.
Perhaps this lady could learn this technique.
Teach the lesson of being caught and you catch them anywhere.