The reservation number part is true.

You can put in a BAEC card if you have one, or a credit card if that is registered as the e-ticket ID, and that will work.

However, if you put in any old card (to start the transaction), and it's not associated, there will be an option to put in your reservation code.

You can do this.

Or, if you don't have it written down, you can put in a bogus code (the people helping at LHR always seem to use 'EEEEEE'.

Then you put in the flight number.

If it matches the name carried on the card you put in... Voila! A printed ticket.

But...

If you have a BP from a machine, you will be flagged for an ID check. The exception to this is UK Dom, for which a credit card is an acceptable form of ID.