Getting back to the specific instance in the OP:
The runner's retouch is not acknowledged and he should be called out on appeal.
5.06 (c) explicitly states:
While the ball is dead no player may be put out, no bases may be run and no runs may be scored, except that runners may advance one or more bases as the result of acts which occurred while the ball was alive (such as, but not limited to a balk, an overthrow, interference, or a home run or other fair ball hit out of the playing field).
All the approved rulings, comments and MLBUM interps that have been cited are given to help us adjudicate the situations in which a runner IS allowed to advance. In the OP, nothing occurred while the ball was alive to allow the runner to advance, ergo, he also cannot correct his missed base.
Another question? Why would you allow the runner to correct his base running error when the defense cannot appeal. Allowing the runner to correct his miss while after time has been called would go counter to the whole basic concept of the "race" involved in the runner trying to correct his error before the defense makes a valid appeal. The cited exceptions to this basic concept (when a runner is awarded bases) even contain the words, "without liability to be put out." This is why the runner can correct his errors during a dead ball award. He has no liability to be put out.