I thought this issue had been beat to death years ago, many times. It's no delusion - it seems clear that the stronger you can swing a bat, the further you can hit a ball.
Take a hypothetical clean ball player who's a slugger who routinely hits the ball to the warning track. Suddenly he decides to start taking steroids, for whatever reason. Once he does this, he can build muscle mass he previously didn't have. The added muscle mass can help the slugger hit the ball harder than he used to. Hitting the ball harder can help that ball travel an extra 10-20' and clear the fence, when it didn't previously.
Suddenly balls that would normally be a regular hit or an out are now clearing the fence. These are home runs that are a result of steroids. Sure, some of that slugger's hits were going to be home runs either way, but now some of them are in question. The mix is unknown.
The steroids aren't going to make a consistent ground ball hitter suddenly start hitting home runs, but they will help a power hitter.