Whoever told you it was an ISH was taking you for a ride. Unless it was a TB that was imported from Ireland which people title “ISHs” erroneously to get more money… I have run across sellers that promote imported TBs as “ISHs” when they did not have ISH papers. They’d say "He’s an irish thoroughbred" as if that classified him as better than an American TB. There is a (IMHO) false belief Irish TBs are better, sounder, and bigger boned than their American counterparts. I don’t find that to be the case especially since several of their top stallions (Galileo, Saddler’s Wells, etc) come from US families top & bottom and are usually sneakily US bred horses. There are great horses to come from both, but I don’t think one is inherently better than the other and they are still, as far as I can see, a very homogenized breed in that the “Irish TB” has not considerably diverged from the US TB at all, and shares many identical sires/dams.
That is very different than the French AQPS, which are often not full TBs at all and usually have Selle and trotter blood further back… also erroneously called TBs by some people but are not.
That being said, not uncommon in any discipline for there to be an identity issue with a nice horse… I remember as a barn worker years ago watching the Very Fancy brilliant chestnut Hanoverian that came right off of the trailer show off in the paddock. Everyone came by to watch him show off and gushed about how fancy he was (and he was!), trainer was saying how he was the nicest Hanoverian she had ever seen, cant wait to compete him, etc etc… Considering I handled his coggins (required at the farm for all boarders) I saw the old owner’s coggins that also said Hanoverian. Anyway you can imagine my surprise when I later saw him doing the flehmen response and transcribed on his lips almost legibly was a tattoo… Barn girls had a blast looking him up, he was a Meadowlake horse. No less fancy but not a Hanoverian. We tentatively told the trainer, who was in disbelief but when she saw the tattoo was very surprised. We don’t know if the old owner was misinformed as well (like in your case) or deliberately lied, but he was a very nice horse.
TBs have such variation within the breed and a non-racing TB looks night and day like a race one, even if it’s the same horse years apart. My TB has the biggest feet on the farm, fistful of bone and a very cobby head. There is nothing about him that is refined. He’s 17h and in no way shape or form resembles a TB, except maybe his eye. His half brother shares many similarities but in delicate, more “TB-like” package.
I would not for a minute discount a horse as not a TB candidate just because he had big feet or was over 17hh. Both are very common in race TBs with some of the more trending sires throwing massive height & feet.