It looks like a double hit, at least near frozen hits, used to be legal in the APA. I just got out a 2003 version of the manual and the definition of the Push Shot shows that a close double hit wasn't considered illegal, but could be considereed unsportsmanlike. I don't know when the rule changed.
PUSH SHOTS: A push shot involves a situation where the cue ball is frozen or nearly frozen to the object ball. The problem faced by the shooter is to keep from pushing or keeping the tip of the cue on the cue ball. It looks bad and is generally thought of as illegal. Push shots are controversial. Push shots will not be called in this amateur League. Even the professional players cannot agree about what is and isn’t a push shot. In general, you can lessen your chances of being accused of shooting a push shot by hitting the cue ball into the object ball at an angle, or by elevating the butt of your cue about 30 degrees. This automatically cuts down the length of the follow through which is the principal cause of a push shot. Players who repeatedly guide the cue ball with force through object balls that are frozen or nearly frozen to the cue ball, using a level cue and long follow through, may be subject to a sportsmanship penalty.