Parma, you obviously disagree with how I would rule this. I can assure you the interpretation I offered is supported by the NFHS Case Book. The key to making this call (in high school rules) is determining the batter's intent.
(As a side note, under ASA rules the batter has done nothing illegal here. The ASA definition of interference says that the player's action must interfere with a defender "making a play". NFHS dropped the "making a play" requirement from their rule book a couple of years ago. In ASA, the batter running, when she is not allowed to, is not interference because the defense is simply not making a play, hence there is nothing to interfere with. This is one point, of many, where ASA rules and NFHS rules diverge.)
Here is the NFHS Case Book Play:
3.6.13 SITUATION B: With R1 on first, B2 receives ball three and begins
advancing to first base as if ball four had been called. R1 advances to second as
if B2 has received a walk. F2 quickly asks the umpire if the pitch was ball four, but
in the confusion R1 advances to second base safely. RULING: The defensive team
should always be alert to the count and attempt plays accordingly. If the umpire
believes the team at bat purposely had its batter run to first on ball three, the
umpire could eject the batter for exhibiting behavior not in the spirit of fair play.
Otherwise, the umpire may warn the coach of the team at bat and eject the next
player to exhibit behavior that is not in accordance with the spirit of fair play. R1's
advance to second is legal.
Note that the advance by the runner already on base is legal. Note that the ruling says the defensive team has the responsibility to know the count and the situation and to act accordingly. Those two premises are universal between all rule sets.
NFHS rules are unique in that they allow the umpire to make a judgment if this act was intentional or not. As a practical matter, an umpire must be 100% certain an act is intentional before ejecting a player. That means he gets to take into account all of the circumstances surrounding the play. Did the umpire give the correct count just prior to this happening? Did the offense do this not once, twice or multiple times? All of that can be considered when forming an opinion of intent.
Proving intent is difficult. Sometimes a player just makes a mistake and has the wrong count. Sometimes her actions might be willful. That is why the ruling allows a warning to be given before enforcing any penalty.
Preventive umpiring- always giving the correct count and stopping the batter if she starts to run when not allowed- will head off any confusion before it happens. If the umpire has any suspicion (which is not equal to 100% certainty), then issue the warning and deal with this accordingly the next time it happens. But to eject the first time it happens is probably going to be an over-reaction.
One more note: The Case Play ruling calls this (potentially) an unsportsmanlike act, not interference. Even if ruled intentional and the batter is ejected, any other runners that advanced are legal, any runs that scored count and the batter would simply be replaced by a substitute who would take her place at the plate to resume the at-bat with the same count. No outs are charged to the offense.
A final comment on your final comment: Yes, there are rules covering a thrown bat that does not interfere with a play. The rules are 3-6-3 and 3-6-16. Here again, high school rules are different from all the others. There is a distinction between a carelessly discarded bat and one intentionally thrown, as in anger. The penalties are different depending on which one it is. Neither results in an out against the batter, but can result in a team warning or ejection.
