That's a big complaint about the "If we have a room...it's yours" statement.
According to SPG terms & conditions, a "Standard" type room must be available in order to redeem Starpoints for a normal free night. The hotel can have tons of other types available, and you are outta luck.
You'll find many old threads here in this forum on this old beef.
You might want to call Starwood reservations just to double check.
Or I believe you also have the option of using additional Starpoints to confirm a Deluxe or higher category of room.