This isn’t as far fetched as you make it sound. Some manufacturers build in more spread from invoice to MSRP to provide greater flexibility in discounting while still leaving the dealership room to profit. Others put those numbers closer together leaving less room.
As an example, pre bankruptcy, it was very easy to get 20% off of a GM product using supplier discount pricing, and even more as employee. Now, that number is halved at best due to GM bringing MSRP closer to invoice.
In other words, some brands can discount more than others. Mazda is more concerned with profitability than volume. This strategy by them can also help resale values.