About a year ago I had a delay of several hours at LAX. Got a text from BA telling me check in desks now close at 2200. Thinking myself safe based on the text, I showed up about 2130 to find the check in desks in the process of closing up and the staff preparing to head home (flight was still as delayed as ever).

If I'd shown up at 2150 I'm not sure what would have happened.

So at an outstation I'm not even sure how much faith you can put in BA telling you to come later. Although there is no conformance as such at LAX, so if traveling HBO it wouldn't be an issue. Can't speak to other non-T5 locations.