In addition to what nux says, what ExpertFlyer shows may tell you absolutely nothing about the chances for award seats opening up. EF does not show BA award availability.

"BA reality" can also differ by point of sale, as is well known in these parts. That can explain some discrepancies between what people see on the internet (especially if doing an unsophisticated search, eg using flightstats) and what BA reality is for the specific agent to whom you're talking.