That is not entirely correct. Most airline CRS will only display a 'maximum' which means there are more than that number available. Usually the number is 7. This means that there are lots more than 7 seats available. It would not do good if a seat availability looks something like this:
F12 J36 Y80 B100 K99 v33

I am merely suggesting that those who get to see the seat availability best are your travel agents and the airlines themselves. But of course, the latter will not tell you how many seats are left on a competitor or their award seats...though AA has been helpful enough to display award seats on Canadian once when asked nicely.