The schools you reference haven't won anything at all in the last 20 years.
Other than the fluke Conner win, who locally has beaten CCH? I went and looked, they've lost 7 times to local teams in the last 7 years(Conner, Ryle(x2), Beechwood, NCC(x2) and Dixie)
What other local team can match CCH's "Local" record other than Highlands?