I think I found the culprit. Commenting two lines got rid of the problem:
procedure TCustomCheckCombo.DropDown;
var aCursorPos: TPoint;
aRect: TRect;
begin
//aCursorPos:=ScreenToControl(Mouse.CursorPos);
aRect:=Rect(FHiLiteLeft, 0, FHiLiteRight, Height);
//FRejectDropDown:= PtInRect(aRect, aCursorPos); //<----
if not FRejectDropDown then
begin
inherited DropDown;
FRejectToggleOnSelect:=False;
end else
if ItemEnabled[ItemIndex] then Toggle(ItemIndex);
end;