Meaning customers would actually turn to a competitor instead because they perceive that if a RZ has some association with the Marriott company (which it does whether they know it or not), then it must be a lower quality property?

Not saying this is wrong (the marketing folks usually know what they are doing), but it is still seems strange to me that a significant number of customers would behave that way. At least for me, not having RZ even in the Marriott booking system makes me less likely to even check them out for a stay.