Yes, agreed.

My take on it
 

See rule 8, section 2, articles 1 and 5 and the lengthy penalty.
8-2-5 If a runner who misses any base ... desires ...he must do so ... . If the ball becomes dead and the runner is on or beyond ... , he cannnot return ... and is subject to being called out upon PROPER and successful appeal.

How did the ball die?

The hitter hit a HOMER. My experience is the ball is dead before the batter ever approaches 2B. UIC should award the batter 4 bases and NOT allow the DC to appeal during this DEAD ball event. If DC has a reason to appeal anything, he MUST wait until the ball is put back into PLAY.

Although FED rules allow a dead ball appeal, the OBR appeal during LIVE ball also takes as much space or more in the FED rule book. The defense must know how to correctly appeal the situation. Some of them boys may need that info when they get to college or go back to OBR play. UIC should make sure they put it to practice in this situation in a high school game too. If the hitter kills the play with a HR, then UIC should NOT allow the DC to make a dead ball verbal appeal. If UIC kills the play, and he didn't in this thread, then the DC may then make a verbal appeal directly to the UIC. But this didn't happen.

FED thing?
 

"Rulebook states that defense cannot get an out during the dead ball because of a HR."

"Could you give a rules reference?"
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OBR 7.05
Each runner including the batter runner may, without liability to be put out, advance_ (a) To home base, scoring a run, if a fair ball goes out of the playing field in flight and he touched all bases legally; or if a fair ball which, in the umpire's judgment, would have gone out of the playing field in flight, is deflected by the act of a fielder in throwing his glove, cap, or any article of his apparel;

FED Rule 8-3, Article 3 ... Each runner is awarded
a. four bases (home) if a fair ball goes over a fence in flight or hits a foul pole above the fence, or is prevented from going over by ...
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The batter who hit the HR must touch all bases legally.