"Breaking" a horse in a bitless bridle?

Yep, bitless or bited, really doesn’t mean much if the hands on the reins are no good.

Pretty much. You can do damage either way, wether the bit is in the horse's mouth or there is a halter on the face. And many people tend to forget that the mouth is indeed a very sensitive area, even moreso than the face because it is an area that is not exposed and therefor has tender skin and nerves. Media and tradition, however, have desensitized people to the idea of it.
Not saying never use a bit, but people should be aware of what it does and how to use it. The really good riders & trainers can ride their horses in a bit or a halter and use very very minimal pressure to get a response, so that they can put a big curb or a double bridle on (for example) and use it the way it was meant to be used; as a tool to finetune a horse's carriage and motion with the littlest pull on the reins and not as a "harsher bit" solution because the handler cannot get their horse to respond willingly.