Fare basis is not always accurate unfortunately in relation to booking class used with some airlines)but most of the time yes). Specially with the "YUP" type fares (or whatever today's version is). some fares CAN book into a different fare class. FF schemes don't care about the fare basis, only the fare class bucket actually booked into. Back when AA sold domestic "First" two class as First booking classes (oh the days gone), for example, YUP type fares would actually book into the P bucket (which, at the time, credited as First under QFF). ie the fare basis might start with YUP..... but booking class was P. These was some time back.
With the AA website, one can select "Details" under the flight number and times info and it will show the current booking class codes for each cabin type. eg:
View attachment 320854
Please note: I am doing this from the AA US website, unlike the AA Australian Website, which has slightly different functionality (and the screenshot earlier comes from - note AUD pricing).
as an aside, most of us find the AA US website far better to use as the AU one can sometimes price much higher on some routes.
personally I find the fare basis discussion to be a bit misleading in the context of points earn. It's all about the booking class.