No it wouldnt bother me a bit in casual use or conversation…
It would only bother me if say …
Horse got injured & nobody was @ the barn but a couple customers. Customers had no idea of true owners identity. Customers then contact “lease girl” who is so possessive she takes it into her own hands to decide horses fate. Hopefully not likely to happen ! Probably not going to happen !
I guess as owner on “some level” I would appreciate to be given credit as the actual owner. Any new lesson person may be a potential lease client down the road. Also if she posts pictures from horse shows I would think it odd if she DOESNT credit the (owners/photographer/horse/rider/etc). I think @ some point I might find it disrespectful if she plastered a bunch of show photos & credited everyone but horse owners. As an owner I may have my own interests to protect - especially if I REALLY needed the lease monies coming. I would want ALL potential clients to be aware that my boy would be available for future lease. But from a stand point that she just casually called him “her boy” - I would just think that normal horsey girl talk & wouldn’t take any offense.
Maybe horse owner or friend could take it upon herself to create a "Barn Newsletter & Blog ? A blog would clarify all odds n ends Something like that might actually be appreciated & well received. BO/BM seldom have time to sit down create something like that.