[Campion]

A valid celebration of the Eucharist can't be had, unless the receiving party has pledged submission and obedience to the Pope's authority over all believers, and the celebrant has valid orders from said Pope.

This is false. Putting it in a blockquote with a citation behind it, as though it had some authoritative source behind it, doesn't make it any less false.

Every Eucharistic liturgy the Orthodox hold is sacramentally valid, according to the Catholic church.

[Kolokotronis]

"Every Eucharistic liturgy the Orthodox hold is sacramentally valid, according to the Catholic church."

And we aren't even remotely under submission to the the Pope nor are we by any stretch of even a Protestant's imagination, obedient to him (though many of us like him quite a bit)!