After a lengthy exchange of emails with a friendly and helpful Customer Service Rep in Dublin, we eventually figured out that the reason why I was not automatically getting Reward Points was because the CDP I regularly use is also defined so you do not get the points.

What surprised me, though, is that if I use our Corporate CDP, for a business rental, I would get the points, but we have a Leisure version (which adds in insurance, for business rentals, the Company uses its own policy), I would get them. One reason why some award programs do not count is to avoid any possible Benefit-In-Kind Tax liabilities, but to bar the points for Leisure use but to give them to us (and not the Company) for business use was a surprise discovery.