Credit for individual segments is not based on the fare basis but on the fare bucket for the specific segment. For instance any Ixxxx fare on BA with segments between London and continental Europe will have those segments booked in J (not I) and credited as such. Conversely, any Ixxxx fare on AA with two class domestic US segments will have those segments booked in A or P and credited as such.

About your other point, the process for credit on partners is always the same with any airline: the airline you fly is the one that has the booking on file (BA does not even know that you have an RJ booking) and you provide the airline with your FQTV number. When you fly, the airline in question will pass on flight and credit information to the FFP mentioning the flights taken and whether the flights are eligible for accrual (small variation if you are on codeshare in which case the operating airline may first communicate with the airline under which code the flight was taken). On some airlines this is done automatically, on others manually (in which case, the airline usually collects the info about once a week and send a bunch of accrual credits to the FFP, I have a feeling RJ is probably a manual operation but I aren't sure). The airline that you have used notionally pays the FFP for the miles being credited hence the airline doing the check (this is unrelated to the accrual rates agreed which may be decided by the FFP or by the airline depending on the alliance - for instance, typically by the airline for *A, by the FFP for ST).

In that sense, the agent's answer makes perfect sense: If RJ said that flight was taken and not eligible for accrual, then this is the information that will have been used by BAEC. Of course, great agents will spot the inconsistency and query it but as a default answer, they would rely on the information passed to them by the airline.