As someone who has leased horses for years, here's my experience:
The shoeing or not shoeing has always been something we CAN discuss. Some owners have a very firm idea of what they want, and I respect that, but it's never caused a problem if I asked why they had that position. If you and the owner cannot discuss such things, then you will likely have other areas with similar tension and it will be a very uncomfortable relationship for both of you. I always say, getting along with the horse's owner is at least as important as getting along with the horse.
I have recently had the opposite situation; I advocated for shoeing Z when he came up off last summer, due to the very dry hard ground and his flat, draft horse feet. The owner had kept him barefoot for a long time, but since she rode so irregularly, him being off much of the summer was not an issue (he was only slightly off and only evident when under saddle at the trot). Front shoes made him so much more comfortable, and ride-able all summer, and I am paying to RIDE him, not just admire him. So, I pay for his shoes. His owner has been super about all of this. I am not just a monthly check to her. I am part of a team that cares for HER horse, so I am also helping her, and she shows her appreciation by allowing there might be a different way to do things, that might be just as good, or better, for her horse.
I do not think the OP was in the least bit arrogant in thinking that she would like to change to barefoot. She might be a bit ignorant of some of the reasons why the horse is shod, and until they have a discussion, she may or may not know the whole picture.