Mr. Warburton's assertion based on the written rules, is absolutely a valid point. But the rule book continues to have MANY inconsistencies. And MLB umpires have chosen to only consider that the runner must advance because the "batter became a runner." MLB umpires then choose to ignore the fact that R1 wouldmight still have right to 1st base until the batter-runner actually reaches the base.
I have seen this called several times in the MLB. Normally, it is on a low line drive to 1B. So, R1 retreats, thinking it is a line out. Then 1B fields a short hop, or drops (unintentionally) the line drive. R1's only hope, at that point, is that the umpire rules an intentional drop.
This kind of picking and choosing which rule to use is actually common. Some of these things are clarified in an interpretation manual or case play book. Unfortunately, this one is not covered anywhere.
So if you agree with the MLB umpires, you are correct. But if you disagree that the rules say this is the correct call, then you are NOT wrong.