So wouldn't that work for both the validity of the consecration at the NO mass as well as the validity of the host in the tabernacle?
I don't see how the two are equivalent. There might be some reason I would walk into an Orthodox church also, but I wouldn't assist at their schismatic Liturgy.
I wouldn't attend (much less participate in) a Black Mass, but if I saw a validly-consecrated Host, I would still show the necessary reverence and attempt to rescue Our Lord from their clutches.
We cannot receive doubtful Sacraments, but the situation here is that we find ourselves before a doubtful Blessed Sacrament.
You might say, "Well, don't go into an NO church." to avoid this scenario, but I can see situations where this might happen, say, if I'm visiting St. Peter's or other churches in Rome on a trip to Italy.