Oooh that is very dishonest. I would talk to her about it and if she gives you an excuse or continues putting you on unsuitable horse's I'd tell her where to go and move on to a place that cares more about your well being than where you are now. Horses are dangerous enough if you are being safe!
There is a saying - green and green equals black and blue. You are correct in that you need to be riding dependable horses who know what they are doing so that you can learn! While it might be "common" for some people - to me it is a huuuuge red flag!! Amateurs in general (ie people who ride for fun) should never be put on anything green unless they are accomplished enough to really ride it. I recently watched a girl on a young horse get bucked off and the horse tried to double barrel her on the way down. The horse bucked because the girl tensed up and that's it. I always think that a rider on a horse should be able to handle anything that horse does. If they can't, then they need to be put on a different horse. There is being challenged, and then there is being plain stupid. Don't let yourself get lumped in the latter category.
I find far more often than not, new riders or new horse people have way more common sense than supposedly seasoned horse people. Just because those of us who have been in the business for a while see stupidity as common place does not make it acceptable. OP, please trust your gut and make a change before you get gravely injured!