If we read the definition of "cancelar" that shows it as meaning "settle" or "pay off", we can see it says:
Pagar o saldar una deuda.
Therefore, for "cancelar" to mean "pay off" there has to be a noun in the vicinity implying an amount that is due and payable, like deuda, cuota, arancel, honorarios, capital, intereses, factura, renta, préstamo, crédito. I don't think "plan" belongs to that group of nouns.
This online dictionary I found seems to be more specific and accurate than RAE's because it does not include the noun in the definition, but only as a reference: cancelar
1 Referido esp. a un documento o a una obligación legal, anularlos o dejarlos sin validez: Si me traslado, cancelaré la cuenta que tengo en el banco. El contrato se cancelará automáticamente al cabo de un año.
2 Referido esp. a un compromiso o a algo proyectado, dejarlos sin efecto o suspender su realización: Si se aplaza el viaje, tendré que cancelar la reserva del hotel. Se han cancelado todos los vuelos con los países en guerra.
3 Referido esp. a una deuda, saldarla o terminar de pagarla: Si ahorro, el año que viene podré cancelar el préstamo.
It seems to me that "plan" belongs to the group of nouns under (2) above.
Note: In the case of "cuenta" (see (1) above), if it means "account" saying "cancelar" will mean "close the account". Instead, if "cuenta" is translated as "bill", then "cancelar" will mean "pay the bill". This verb is indeed a tricky one in Spanish, and we have to be very careful because it may lead to confusing and risky situations: for example, if we say cancelar la póliza, that means "to cancel the policy" so that it is no longer valid or in force; instead, if we say cancelar la prima, that means "to pay the (policy) premium", so the policy continues to be effective. I think this confusion might account for what happened to the OP when he says: Well she wanted to pay the service, but they could have made a mistake and cancelled it for some reason.