My interpretation from the BA website is same as the OP's ie that this device should be allowed.

I've noticed a quite relaxed attitude to iPods as well on BA. I've been asked to have them off for the safety announcement and for landing but only so that I would be alert to what's going on around me. Inflight obviously never a problem.

But as others have mentioned their own other airline experiences, I'll contribute my own. I had a funny argument with a Lufthansa cabin attendant 1-2 years back while standing in the aisle waiting to disembark (ie after engines had been switched off and doors opened): she was trying to persuade me that using my mobile phone was strictly forbidden because it ran the serious risk of setting the whole airplane on fire

I didn't persist as my checking voice-mail could be postponed....also my ambition stops short of trying to persuade a well trained flight attendant that what she's been told is technically impossible and the rule plain silly