It's not really clear what FCM means by front/rear bounce rate. From what I know (reference below), the bounce rate is related to how we derive the bounce and pitch frequencies and centers for the coupled front-rear vertical motion of a car. There is not a front and a rear bounce rate. There is just a bounce rate.
The vehicle bounces (up and down) and oscillates (rocks back and forth) about a bounce center and a pitch center, respectively, at a bounce frequency and a pitch frequency. These two modes are superposed to give the final motion. Given the specifications of the vehicle, one can calculate the centers and frequencies and these properties have an impact on comfort.
Cars have higher spring rates in the rear than in the front because it minimizes the pitch motion which is the most annoying mode. According to design principles, not only should the rear rate be higher, but it has to be 30% higher - or the spring center should be at least 6.5% of the wheelbase behind the CG. There are also other guidelines as quoted below. So the "Flat Ride" concept might be vaguely related to these guidelines but it isn't 100% defined by them. "Flat Ride" isn't something that's defined in any vehicle dynamics textbooks, as far as I know.
These principles affect only the ride quality and are unrelated to the cornering ability. I think it is safe to say that cornering ability usually comes at the cost of ride comfort.
Here are the derived design principles from the source mentioned below:
Source: Gillespie, Thomas D., fundamentals of vehicle dynamics (relevant chapter available here: https://edisciplinas.usp.br/mod/reso...php?id=2960518
The relevant portion starts on page 175).
And since I said this was not related to cornering ability, here is a quote from a famous book (Tune to Win, Caroll Smith) about what an experienced racing engineer had to say about spring frequencies.


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