wrote:
I can top up a mobile phone at a cash machine. They need to know who
I am to charge me but the phone I'm topping up may not be registered
at all and has no problem being topped up. Same with Oyster cards,
They need to know who you are - and the phone number.
Or the Oyster card number.
No difference.
Er, obviously you have to give the Oyster card number, but why a phone
number? The cash machine warns you that the money's gone anyway. No
follow-up if the top-up fails.

Context is all:
phone number for the phone you are topping up
Oystercard number for the oyster you are topping up.
--

Andrew