Can a 2 ball playing matchplay play with 2 ball playing medal?

[Curls]

I only allow 2 ball KO's to go out and play a stableford. If a 2 ball match is playing with another player who is just in the stableford then there can be a disproportionate advantage for 1 player who is getting reads on the greens for their match.

I don’t really get that, surely by that rationale someone playing in a 4 ball has an advantage over those playing in two balls, but no one prevents that from happening

As it happens we just played straight matchplay on our own, it was quietish so we got around ok, we got through two 4 balls and having the option to pick up sped up that process