It really is the way to travel isn't it? I've got to tag along on some corporate trips in the past and now fly a little airplane... no luxury but I'll take my way over an airline any day*
When I last flew down to Mexico the airport of entry I used had no airline service. So, there was no difference and I think all flights were equal for customs & immigration purposes.
I suspect that the outfit you chartered (?) the flight through probably paid for a 'handler' to take care of the logistics in Mexico. I would not be surprised if the handler greases wheels/pays people to get their clients to jump the line. I'm not saying its right... just my suspicion of how its done. There is no overt need to use such a handler, but if not, your flight crew probably would have to have coordinated your arrival with the customs (did they use the traffic signal there?) & immigration folks.
* Any day the weather isn't too bad.