I believe that the 3/4" thick rule applies to Critical Mail (and no, I am not sure what that is) ... and also to distinguish between "flats" and "parcels" in First Class Mail.
If you poke through all the details of the DMM it does not specifically mention a thickness for the FREs.
So that "Customer Mailing Guide" is adding to the confusion.
That said... it is certainly possible that the Post Office will at some point change the rules about the FREs. If they do, my hope is that they will publicize the change far enough in advance that everyone who uses the FRE service will not be caught off-guard.