Ah, the old provocateur raises his head again.... ;-)
I don't know that there's any easy answer to your question, because the underlying subject has to do with trying to define the thin line between God on one side, and human teaching about God on the other. Church rules are intended to define that line, and as such they're more than just "rules" of the sort you find in a kids' game. "Proper" rules are considered to be given by God.
So it's difficult to distinguish the two parts of your question. Overall, I'd say that the answer is basically "yes," to both.
First, the context:
The fundamental purpose of the church (in the universal sense of the word) is to ensure that what Jesus taught to the Apostles, is accurately passed on trhough the generations. That's what doctrine is all about -- a set of rules and processes designed to keep the Message free and clear of "innovations" that are not part of God's teaching.
However, churches are human institutions, and subject to human failings that get in the way of things. (For a secular comparison, see how our Constitution has been warped over the years.) The message gets obscured, either by false teaching making its way into the mix; or true teaching being wrongly identified as "false" and rejected.
So in that context, the Catholics are saying that they're the keepers of the true teaching, including about the Sacrament of Communion, and thus the only true Communion occurs in the Catholic Church.
So to answer the first part of your question, it's more a matter of receiving Communion in the right way, of which there's only the one (Catholic) option. The distinction is perhaps subtle, but it's important: it's less a matter of excluding other churches, as it is saying that Catholics offer the only true Communion.
In that context, we see that it is a "Church Rule," but that rule is intended to properly identify the exact location of the thin line between God and man.
OK, thanks
Your 64 is well put. Of course, I’d come at it from the other side, but the core explanation is valid.