I think the confusion arises from the verb 'to insist'. It's similar to 'to
know'. Look at these two examples:
I know him.
I know he is late.
If the object of the verb is an independent clause (he is late), then the
subject of that clause (he) stays in the subjective case. The quirk with
insist is that it can also govern the subjunctive mood (so "is" changes to
"be"), but we ignore that when looking at the sentence structure.
She insisted that WHO be on time? [correct]
She insisted that WHOM be on time? [incorrect]
The trick is to look for the object of "insist".
Whom did she insist be on time? [incorrect]
The question above feels right instinctively, but it isn't. You need "Who"
to complete your object "Who is/be on time?"
Great question. I think I've got the right answer, but I would be happy to
consider other versions. I think the "know" examples make it a little