The Brian Gym is a glaring example of a completely unproven theory about learning and development. Learning is full of theories that range from the complete nonsense of the Brain Gym through interesting, but unsubstantiated, ideas such as the hundreds of different learning styles (Kolb etc) to rock solid cognitive psychology (Ebbinghaus forgetting curves). Sitting to one side are a myriad of common-sense rules of thumb and folklore based on experience rather than science - don't lecture for more than 45 minutes, when asking open questions have a closed question to back it up, etc.
The problem I find is that there is a kind of inverse correlation between veracity and utility. There are a few facts from cognitive psychology that are true, interesting and useful - the limits on short term memory for example - but precious few . On the other hand, VAK is scientifically highly dubious - but you can actually use it as an inspiration to make your courses more varied in their use of media and remind you that people do learn in different ways - even if it is not a fixed characteristic of a particular person. It is a productive way of thinking about courses and teaching.
What would be great would be a body of useful, interesting and incontrovertible knowledge. But can anyone give 10 facts about learning that are:
Interesting - not something that is obviously true
Make a practical difference to how we design or deliver training
If not, then we have to go beyond the scientifically established to say anything interesting about training - a melange of home grown wisdom, interesting concepts and the occasional fact - hopefully held together with some straightforward logic.