Yes, that is the "proper" way to mount a horse based on a silly tradition. I, like others, believe that it is important to be able to mount a horse from either side. You never know what will happen and there have been times where I HAD to mount on the horse's right side.
Also, I am a firm believer in always using a mounting block. Mounting from the ground is not good for the horse's back from the constant pulling. Plus, why make things harder on yourself when you can use a block? I do think its important to be able to mount from the ground, but even when I need to dismount on a trail, I will look for a close by tree to use. Only if there is nothing I can use around me will I mount from the ground.