The technical person--very friendly and probably located in India--tells me the reason I cannot use OLCI is that my ticket was never issued. Even though I bought it on BA.COM, when the date of the outbound leg was changed in June, the agent somehow messed things up.
I'm glad you sorted things out in the end. The above is a veeeeeery common problem for me. It seems like anytime I make any changes to an e-ticket, I have problems of this sort to the point where I now get my agent to call BA to make sure their systems are correctly picking up all changes. You'd think that schedule changes on an e-ticket would automatically trigger a ticket re-issue but alas it doesn't seem to be that way. And many agents don't seem to know that they need to manually force the change.
As for the cheap excuses you got from the various people you spoke to, typical really, isn't it. Insufficiently trained people who make up things as they go along. Guess the majority of passengers put up with it or someone would have changed things by now.