No, standby works the same. What the text on aa.com means is that if there happens to be a sAAver seat available, you don't need to standby, you can confirm the change for free at any time (since aa awards have no fees for date & time changes). If not, then you standby.
Originally Posted by aa.com
Passengers traveling on unrestricted Y fares and AAdvantage AAnytime travel awards have the flexibility to change flight arrangements at no charge. Passengers traveling on AAdvantage MileSAAver awards continue to have the flexibility to change the date/time of their flights at no charge, provided award seats are available on the desired flight.
... is in addition to, not instead of, the usual standby rules.