That's not true. The World Standardized Rules do allow for the cushion/ball/same cushion scenario for a legal hit. See the provision below from the applicable rule posted earlier by dogsplayingpool.
"A ball which is touching a cushion at the start of a shot and then is forced into a cushion attached to the same rail is not considered to have been driven to that cushion unless it leaves the cushion, contacts another ball, and then contacts the cushion again."
APA rules on frozen balls do not have such a provision.
You're right. I didn't notice that he said if it hits another ball. I thought he only said cue ball and object only. My mistake.