Not even close. "A" fares actually were full fare domestic first class fares not too long ago. "F" became full-fare domestic in preparation for joining the Star Alliance, and "A" became a discounted domestic first class fare bucket, although most domestic fares booking into A actually had fare basis codes beginning with "BUP".

Also, following the last fare class re-mapping, both A and Z fares were used for discounted BusinessFirst. The "A" fares were the cheapest, and did not earn the 50% class of service bonus miles. These corresponded to the old "R" fares.