Further, I asked if she (the agent) still showed open seats in business. "I show around 7 or so, sir," she replied. "Seven? There are 16 open on AA.com." "I'm sorry sir, we're not allowed to give seat counts out over the phone." "Well, should I trust AA.com or leaning towards more what you say?" "My advice would be to stay up to date with AA.com" and there was a slight giggle. What gives with that?
When you say there are "16 open on AA.com", are you looking at the seat map? The seat map only shows which seat assignments have already been pre-reserved and is not indicative of how many seats are actually available for sale. It's possible that there are people who have bought tickets but have not reserved their seat assignments yet.
When an agent pulls up availability, if there are 7 or more seats available in a given inventory, 7 is all that will be displayed. The agent won't know if there are actually more than 7 seats available until she tries to sell more than 7, hence the reply of "around 7 or so". Not only is the agent not permitted to give seat counts, but she's unable to do so in the first place.
My advice would be to invest in an ExpertFlyer subscription so you can check availability for yourself. In many cases purchasing a load factor-based upgrade outright is a better value than using miles + copay, and both come out of C inventory.