I have no doubt you are right and there are horses out there that are unknowingly not quite what they were claimed to be. But I would imagine that the statistics are not quite as high as they are for people (1 in 20 - wow, that’s a lot - Cheating is rife).
I breed warmblood x Thoroughbred horses (only a one or two each year at most) and I often look at the foals I breed and think, mmmm that semen I imported really could have been from any horse - and I wouldn't know unless I did further checks!! LOL!! We are relying on the studs integrity and efficiency at having sent the correct semen (and our vets to inseminate the correct one too). Definitely room for error to occur, hopefully not 1 in 20 though! (I don't DNA check my horses foals, but if something that didn't look right came out I might... a pony or coloured horse? He he). But I would be very happy for anyone to DNA check them before purchase... no-one bothers though, because if the horse can really move and jump - that is what you are paying for. Different then if you want a "pure bred" Arab for showing. Most horses I sell, people dont even remember who it was that I told them the stallion and mare lines were and don't really care. It is only if they decide to breed later with a mare that I may get a phone call to remind them of the parentage. My mares are thoroughbreds, but are warmblood foundation mare registered too just in case anyone does want to register a foal.
However, I have little doubt as to all my ex-race mares parentage. The racing industry in Australia take few chances, and I assume this is the same in most countries. When dealing with the massive stud fees of a racing Thoroughbred no owner would leave anything to chance. With stud fees commonly in the tens of thousands AND for the good sires, hundreds of thousands... Would you leave anything to chance?? No horse can legally be registered or race in Australia until an independent vet has blood typed it to match its parentage. Also there is no importation of semen in the racing industry here yet. Every race horse has to be conceived naturally (hence the existence of shuttle stallions from overseas). This is to limit the chance of a mistake. I worked on a large racing stud many years ago that stood 6 stallions and had approximately 380 mares to serve in one stud season. Every mare wore a tag around there neck and the tag was checked before they were served, as were brands and markings via the mares papers that always accompanied her. It was quite amazing how efficiently and well set up these big studs are.
All day, everyday for three months every year was spent teasing, serving, and scanning. I never recall an error. So I would say if you have a thoroughbred with racing papers, you need have little doubt. I would imagine DNA testing may come into it these days, I am not sure anymore? It was 10 years ago that I worked in the industry. They were all just blood typed to confirm parentage then.
Most other studs simply don’t have all these checks and balances in place the way racing studs legally HAVE too. Some do by choice I realise, but not the majority, In fact with warmbloods if you by three straws of semen, and get your mare in foal with just one, you are allowed to inseminate any of your other mares if you feel like it with the left over straws or sell them on – no extra charge, no need to register any of them if you don’t feel like it, because with performance horses (dressage, showjumping, eventing) no-one cares quite so much how they came about so long as they can do the job (it is a good idea to keep a record of parentage of course). “Mutts” of both known breeding and unknown breeding are common place in the performance horse world :)
EDIT: I should add that I only breed quality horses, none of the offspring of which are purebreds and all of which are bred to perform, out of mares that have proven themselves to me in competition and soundness. I have no interest in purity - that means nothing to me or to the world of eventing. Can the horse move? Can it jump? Does it have good conformation and a good temperament? If not... then in the performance horse world, it won't matter how pure and how many DNA tests it passed... no-one will want to pay much for it. Most of the top performance horses in the world today (warmbloods) are of mixed heritage and would not be considered "purebreds". If we found out today that a stallion like Donnerhall was a "mistake"... we would still breed to him because of his type and what he throws.
EDIT: Tina C - Did you mean you worked at Blue Hors Stud?? (Your spelling is wrong?). I looked at a stallion they stand called Blue Hors Romanov... link....
http://www.bluehors.net/cms/index.php?idcat=23&changelang=2
And Blue Hors Hotline (I posted a link to one of his beautiful sons recently).
I cant imagine that they would not give a 'free return' or money back for a mistake like that?? If I got a grey foal from semen from him to my bay mare - I would definitely want compensation such as a free return or my money back. They would not have a leg to stand on and would be leaving themselves wide open for litigation otherwise!? Dissapointing to think, I as a small time (mainly for my own use) breeder, am so careful and honest, that a large stud such as them, would do be so careless and then fail to take responsibility.