But think about it from the WC/Warden perspective. DuMorne is dead. This guy was a badass Warden: he was in on the Kemmler finale! And that was 40 years ago... presumably he's only honed his art further.
Do they believe that a punk teenager beat DuMorne in a duel?
A punk teenager who was under supervision by DuMorne, without much opportunity to learn/practice black magic? And presumably without resources (books/etc) as DuMorne would have controlled such things.
From the WC/Warden POV, this premise seems absurd, a non-starter. In their shoes, I would presume another party, a 2nd wizard; even if Harry was the proximate killer, who was pulling Harry's strings?
If DuMorne could be killed -- a top-tier combat wizard -- then nobody is safe. That (presumed) 2nd wizard must be discovered, or be proven (beyond reasonable doubt) to not exist.
And it's that investigation -- of the grounds where DuMorne lived, of the mundane records such as school enrollment, etc etc etc. -- where I think Elaine's existence would have come to light, whether Harry tried to conceal it, or not... or was never even questioned on the matter.
I do not think anyone would be looking for another wizard. I think there were probably 2 groups those who trusted McCoy completely and those who just figured Harry took DuMorne by surprise. Dumorne happily giving Harry a lesson. Harry draws in lots of power to, Dumorne thinks, cast the practice spell. Suddenly fire coming right at Dumorne and he does not get shield up in time.
That group probably figured it would happen again with McCoy. Either McCoy would kill Harry or if Harry pulled it off again they would kill Harry afterwards and would not have the annoying McCoy around anymore.