I haven't read (or know about) the story you mention in the OP, but my understanding is that BA check-in staff have access not only to Timatic (although when I emailed BA to ask what they check, they told me to use https://www.iatatravelcentre.com) but can also phone a competent department which carefully checks validity.

In other words, turn up to the airport in plenty of time and even if check-in staff are confused it should get sorted out.