An official's judgment.

And kicking an opponent can easily be considered fighting.

Read the definition for flagrant foul (applies the same whether personal or technical). I don't have it in front of me, but I recall the word "savage" in there somewhere.

Definition notwithstanding, don't forget that fighting is a flagrant act, and any actual punch, kick, strike, etc., or attempt therein, is grounds for calling a flagrant foul. I had a similar situation in a JV game last year. Player got blocked (personal foul called) and after both players ended up on the floor, he tried to kick the fouler. It wasn't terribly violent, and he didn't make contact, but I penalized the intent as a FTF (now part of a false double).

As to the OP case, we can debate severity and intent all day, but we weren't there in the arena. The game temperature seemed to be getting a little high, so that might have been the reason for the quick flagrant trigger. I've got the official's back here. Where I'd criticize him is how he quickly left the scene to go report to the table. He's lucky a fight didn't break out behind him.

NCAA rules apply here
 

In New York, girls basketball is played under NCAA women's rules, so "disqualifying foul" is the correct term and rule, not flagrant foul.

NCAA rules give wide authority to the official and include fighting and flagrantly contacting an opponent among the reasons for calling a disqualifying foul.

The "disqualifying foul" is a new term this year, replacing what used to be a Flagrant 2 foul. The NCAA even offered printed guidelines in judging a disqualifying foul.

Neither the judge nor the school superintendent have any business getting involved in this decision. Shame on both of them.

After having watching that video probably 20 times I would have gone with regular technical foul. The first few times I watched it I thought that was what was called and just assumed it was her 2nd. Disqualifying technical seems excessive.

That being said, parents who bring this stuff to court are jackasses. And probably the kind of parents I end up ejecting from 4th grade Rec games for their shenanigans.