There's nothing contradictory between the manual and the post you linked. The atc_parking_code in the aircraft.cfg, as explained in the manual, only affect the choice of ULD loaders, and doesn't have any effect on the ground operator.
The ground operator, instead, is chosen using a scoring system that takes into account the couatl.icao_prefixes lines in the SIM.CFG of all GSX vehicles. Only the operator with the highest match will be show.
The atc_parking_code in the *scenery* (AFCAD), are used ONLY as "tie-breakers" of ground operators having the same score. This means, if the scenery has set for a certain parking atc_parking codes that don't match anything in the GSX vehicles for that airport, they won't do anything. To see an operator, it must have some score for that airport in the GSX vehicles files and, if there are many, only the one with the highest score will be chosen. The atc_parking_codes will enter into play only to break ties.
However, with the GSX customization page, you can use the "Airline codes" parameter and, in this case, the codes specified there will take precedence over everything else. But you must set them YOURSELF. If you don't do that, the ones from the scenery AFCAD will be shown, as an information, but they will only work as tie-breakers. It's only after you *edit* the field, they'll become real overrides, directly affecting the choice of operators, regardless of the default scoring system.