I have read the faq and googled a bit but was not able to figure this out.  What I am trying to determine is how do I prove to someone via email or their e-commerce website that it was me that sent btc from wallet xyz?

  Is this only possible if the recipient generated a one-time address for me to send to that was presented to only me?

  Or from the merchant perspective, if I advertise wallet number 1234 and a customer sends me an email with an order for a widget and a claim that they sent me payment from wallet 5678, how do I know that the person sending me email sent the payment from 5678 and not someone monitoring the distributed ledger for payments to me?