There's really two answers to this question - the answer that normally applies, and the real answer that rarely applies...
Whenever you purchase a ticket with United, during the process it will often advise you that "The credit card used for this purchase must be available at check-in". In theory at least, if you are unable to provide the credit card then you will need to provide another means of payment, or you will not be able to fly.
This requirements exists as an anti-fraud mechanism, to stop you purchasing a ticket with (for example) a stolen credit card number.
In practice, this requirement is not normally enforced - but it does happen. If you search Google for the above phrase you'll find a number of forums discussing this requirement, and a number of reports of people being asked to show their card.
Presuming that you do have the means to pay for the ticket at the time you fly (eg, if you have a credit card - even a foreign one) then I would say it's worth the risk. In the unlikely event that they do ask to see the card and you can't provide it they will be able to refund the original card and charge the amount to the card you can provide.
I've just checked the confirmation email from a recent booking and it also includes a reference to this.
Airline tickets are nontransferable. The name on your ticket must
match the name on your government-issued photo ID presented at time of
check-in. You may also be asked during check-in to present the
credit card used for purchase.
(Bolding mine - in the actual email the bolded text is shown in red!)