If there were no runners on would a centre fielder with ordinary effort have thrown the runner out at first? No therefore the batter should have been credited a hit.
To me any hit to the outfield that results in the runner getting on is a safe hit (unless its a muffed fly of course)
The example of the ball dropping and the runner getting caught out at second. Would the batter have been out at first with ordinary effort? If the answer is no it's a safe hit.
The fact that a batter might've been safe at first is irrelevant, IMO. For example, let's say you've got runners on first and second, and the SS or the 3B makes a diving stop and has only one play - to third base - to get the out. If the defense makes that play, it's clearly a forceout and not a base hit, even if the batter had crossed first base before the out was made. Wouldn't you agree?
To me it would be a fielders choice, unless the base runner on 1B did something boneheaded, which would result in the batter being credited with a hit and an error on the base runner.
That sounds fair, but not legal. A runner can't be charged with an error.
IMO, the ASA is clear on this when it states: "A BASE HIT shall not be scored when a runner is forced out on a batted ball or would have been forced out except for a fielding error.''