How are we to know that a Reservist was, in fact, a) called to active duty, and b) served the full period for which called? Don't some Reservists just receive a letter telling them they are being placed on active duty?

A Reservist will always have orders placing him (or her) on active duty -- (it is the only way the Reservist can be paid). While the individual may also have a letter saying that he or she is being called up, there will always be orders backing this up. Similarly, when the Reservist is released from active duty, he or she will always have separation or demobilization orders.