I didn't see the press conference or read the transcript, but I can't believe this is accurate. It's actually impossible for him to know that. He could only pick one player at number 1, so there is no way for him to be sure that player will be available at 3. This is just talk.
The actual quote is:
We think there’s a really good chance the player we’ll take at 3 is the player we would have taken at 1
The thread title cut off the qualifiers on it. He's acknowledging that the player he would have picked at 1 might get picked at #1 or #2
Presumably, Ainge would have asked Philly to disclose their pick before agreeing to the trade. Thus, it's really just the Lakers we need to worry about. Considering this is Magic's first draft and first big decision, I'd have to imagine he won't defer to his subordinates and will draft Ball. Thus, if Ainge would have taken anyone save for Fultz or Ball #1, his comment is likely correct.