My take on the ABA rules was that birds caught in the nets wouldn't be countable, but after they were released and shaken off the effects of being captured, they would once again become countable. You can't count the birds immediately after release, but once they're back to normal behaviour you can count them. It may not be that simple, but that was my take on it. I don't count birds so my spin on this doesn't really matter, but if I saw bird X at a banding station and was pretty sure that I would never get the chance to see/count that species ever again, if it was possible I think I'd make the effort to get that bird on my list, even if it meant trying to track it for a few minutes after being released until I was comfortable that the bird was no longer under the influence of being confined. Admittedly, MY comfort level in making a call in that situation might not measure up to someone else's comfort level in the same situation. That same comfort level might also be influenced by the value of the bird wanted for the list, too.
Having said all that, I wonder if the best approach might be to focus on the birds before they get caught in the nets.