False.

Just go to aa.com and go thru the process of booking an SAAVer award to see the fare rule for the award. You will NOT find any restrictions along the lines of No value unless cancelled before departure.

Done it first hand several times with domestic AA awards when I wanted to do a same-day standby on later flight. Didn’t cancel and showed up 6 hours after original flight and placed on standby no questions asked. I usually try to call AA and let them know of my intent to do a later standby but a recent trip involved a 30 min hold time only to get an AAgent who tells me standby not allowed for awards and was even very apologetic about it. I didn’t have time to educate her on policy posted on aa.com and simply thanked her, hung up and no showed the original flight.