changing bridles

Just today I was riding my ex-racehorse thoroughbred, and she was shaking her head around and being a pain about giving to the bit, so I thought, "maybe I'll try riding her in a snaffle bit with rings instead of shanks." Well, I was doing a bit of reading, and I came across this blog that gave some pretty good reasons for not changing bits. This trainer said that if you have hard hands, you make your horse have a hard mouth so that when you move to a harder bit, the horse becomes hard to that too. So now I am rethinking about changing bits even if I am getting one that has less force. It could be my problem, not the horse's, so I will try to fix my problem first. I have another horse that also just is not much fun to ride in a bit, so I ride her in a ballero, which is basically a halter. What she does is throw her head around and constantly chews on the bit. This got me to thinking that that's kinda what a green horse does when first introduced to a bit. So know I am thinking about just putting a bridle on her so she can get used to it being in her mouth.