If it had black legs/mane/tail, zebra stripes, and a dorsal stripe whoever registered it as a red dun had no idea what they were talking about.
Red dun is basically a chestnut horse with a dun gene, they won't have any black markings. A bay (or zebra) dun is a bay horse with a dun gene, they have black markings. My horse is a bay dun and my friend has a red dun. Their coloration is nothing alike, except that they both have zebra stripes, dorsal stripes, wither marks, mask, etc. The red dun's dun factor markings are all a deep red color and Soda's are black on the legs and reddish on the rest of the body (because the black is restricted to the points due to agouti).
Any color guru is free to correct me where I got something wrong, I know I don't know everything about color.
Soda - a bay or "zebra" dun
Dangit I don't have the pic of my friends horse on the comp. Let me look