The Versatile rule requires that the interpretation be "The enemy model is considered to be engaged [BY THE VERSATILE ARMED FIGHTER], but may not in turn be Engaging [WITH] the fighter armed with the Versatile weapon" because the reverse makes Versatile entirely non-functional. If Versatile only makes the TARGET count as Standing and Engaged, but not the wielder, then it can ... never be used. At all. Because the attacker will never be Engaged, and thus will never be able to use a Fight action at Versatile range. At all.
If your Arbitrator is choosing to interpret Versatile such that "The enemy model is considered to be [Standing and] engaged, but may not in turn be Engaging the fighter armed with the Versatile weapon [who is thus not Standing and Engaged]", Versatile at your table can simply never be used. At all.
Yes, that text is not clearly written, especially for those of us with English as an additional language. But the intent has been made clear that it is the fighter armed with the Versatile weapon who counts as Standing and Engaged at versatile range, and not their target instead.