I'd say it depends a lot on what she meant by "hurting". For example some people smack horse when horse try to bite. Is is going to hurt the horse - no. But it'll be unpleasant and bossy and will teach horse. I've seen people turning back on horse and kicking at them to show who's the boss. Will it hurt the horse if you do it with sport shoe on - I don't think so (of course I'm not talking about kicking horse, say, in private parts or something, or doing it really hard). On the other side there is such thing as cruelty, when horse CAN be really hurt intentionally (say beat up with the whip and so on).
I knew the guy who said same thing as your barn owner. But he meant that if you smack the horse as panishment it's not going to hurt it. He didn't mean cruelty at all (very gentle with animals guy, btw).