Counterchanged flags

No. All that is required is that the tincures are swapped charge for field.
See, for example, the Welsh badge I already showed,
quarterly Or and gules, four lions passant guardant counterchanged
or the arms of Lord Peach " Per fess Or and Azure the Sword of Mercy erect pommel in base Proper between four Stafford Knots all counterchanged"

I was going by the description in Wikipedia. Perhaps I misinterpreted it.

And I’m going by how several actual real arms are blazoned.