It sounds like he was having trouble with the system or it was down and he was just attempting to log into your account through the website. 10/10 for going to the effort, but 10/10 for stupidity.

On the off chance this gent was collecting all your ID information for his nefarious ways then I would contact BA about this. Though not to OB, just in case he intercepts the message (*Jack Bauer mode off*) - maybe write to Willie Walsh's office.

EDIT: Or contact our BA.com helper