If you had a problem with a booking on ba.com that was made with any of the above payment methods would your contract not be with ba.com and not the organisation that processed the payment ?
Yes it does. However, under UK legislation, if you buy an item using a credit card and the transaction goes awry (eg your card gets account gets charged twice) then the credit card operator must assist you to obtain a refund, whether goods, services or travel tickets. In a case disputed by both parties, the credit card operator will usually place the money in a suspense account and appoint a mediator.
By using PayPal for the purchase of items excluded specifically from their "User Agreement" the consumer has unwittingly destroyed his consumer rights. As a company registered in Luxembourg, a country with questionable scruples when it comes to matters fiscal, the UK has very little influence over their trading standards.