As stated above, 'foreign' managers have been a much more recent thing in the Championship than in the Premiership. To compare it to as far back as 1992 (even though I compared the relative crapness of 'English' manager since then - the Scots seem to make better managers) is unrealistic as there...
You've argued the point yourself - the relative number of 'foreign' managers in the Championship is miniscule.
It's not damning at all - it's on a par.
Since the start of football - in 1992/93, obviously - the following numbers of trophies have been won by English managers...
Premier League / Premiership - 0
FA Cup - 2 (Royle 95, Redknapp 08)
League Cup - 4 (Atkinson 94, Evans 95, Little 96, McLaren 04)