I'm in the "should have been allowed in" camp.
Pax was eligible to enter. Lounge wasn't full.
Ultimately who is the dragon to decide whether the lounge is or isn't going to fill up? BA flight could have been delayed en route, or half the pax could have decided to go shopping at ORD airport and not use the lounge.
BA may well have the STA caveat, but I think "subject to whether the lounge dragon thinks the lounge may or may not become full" is pushing it.