In particular, must a cognitive theory about memory that would please you be stated in a way that could be tested by brain scientists?
Sure! But an even better idea might be to demand that a cognitive theory be stated in a way that the Almighty himself could pass judgment on.
Legendary memory researcher Endel Tulving setting high standards, from p93 of Conversations in the Cognitive Neurosciences (ISBN 9780262571173).
Mind Hacks 