I worked with TB's 8 years, broodmare operation. The mares have to foal in the state in which they were bred, for the foals to be eligible for the breeder's monies, (think that is what they called it). If your mare was bred in KY, or FL in our case, you trailered the mares down to FL well before they foaled, they were then bred back and you went back and got them in a couple of months. Foals stayed with their mothers, on their mothers.
Broodmares were just that, broodies. Didn't go back to racing. There might have been an odd one that did, but by and large no.
And we hauled mares/foals just fine, nothing against it mandated by the JC. Mares were taken by the barns that were providing mare care, to the farm where stallions were, and teased, bred if in, and then taken back to other farm. They generally stayed down there 3-4 months, from time mare in foal was hauled, to when I went back and brought them home.
Don't doubt that some of this is going on, but don't know about the numbers reported? But do know one thing, if a human can make money of the misery of a living creature? They will do it.
And most mares will NOT take another foal if they have their own. It is a rare one that will. And nursing two usually means one doesn't get enough to make them really thrifty, this is why it is such a bad thing when twins are born, and one is usually smaller/doesn't do as well.
Horses make me a better person.