I can only talk about my personal experience with proprietary directors. I spent 7 years in accountancy practice, during which time I dealt with well in excess of 100 client companies. I cannot remember a single instance where I encountered a proprietary director who owned over 15% of the share capital, but did not exercise any control.
I now have a different job, and it regularly involves looking at company directors and their relationships with their companies, and again I'm genuinely struggling to recall a situation such as you describe (at a conservative estimate, I've looked at another maybe couple of hundred companies).
I reckon that the number of people who fall into this category (not actually exercising control, but denied a PAYE credit) is miniscule.