Well sounds like you trying to use Southwest rules on AS/AA tickets/metal. Both AS and AA are more flexible about standbys except for a very limited type of tickets they sell such as Web Specials, Site59, and specific time restricted tickets (6-7 AM, 7 PM+).
You have asked Southwest about standbys. Southwest are all about squeezing money out of you after you purchase your cheap fare. If you get angry and decide that you won't fly Southwest again they don't care they have their business model like many other companies (i.e. some discount retail stores are very difficult about taking returns back and compare that to a Costco or Nordstroms). Between the two (AA and AS) I would feel very comfortable about standing by as long is it is on the same day to the same place (or co-terminal with AS) and I would do it in an instant to save $100. What complicates things is if something happens (as is just happened to me so luckly I was confirmed) and suddenly every flight for the rest of the day is overbooked.
It is funny you mention about what Southwest would do. They are a joke and they treat their PAX like trash. Need evidence - watch the "Airline" program.
A rencent flight from ORD - SNA on AA they actually put "Priority" on my standby because 1) I had missed my 6 AM flight
and 2) I went to the AA Club to get on the list.