As far as I knew they're not really sure of the genetics of Brindle actually. It seems to be slightly inheritable from what I've heard. The Brazilian Warmblood that you showed is a stallion and apparently one of his was born with some brindle patterning but it appears to be fading (although we all know how foals coats can be a bit misleading at times) but heres what it looked like when he was born:

Also this website:
Brindle Horses - a rare equine coat color
Has hereditaryily (is that a word?) produced brindles. As seen with this chart-thing:
http://www.geocities.com/sbatteate/b...ped/webped.htm
So it appears to me to be a gene based as well as chimeric as like Dunbar's Gold they do seem to pop out of no where.