No, that is not what I said. I said that communion with the Catholic Church is one of several criteria in order for one to receive Holy Communion at a Catholic Mass. Another criterion is that a Catholic must be in a state of grace (or as you put it "in communion with the Lord") in order to receive Holy Communion. This means that if one has committed a mortal sin (committed a grave act with knowledge - that it is a grave matter - and full consent) and not gone to confession, then one cannot receive Holy Communion. If one's soul is in a state of mortal sin and one receives Holy Communion, then one has committed a sacrilege which is another mortal sin. Catholics who are not in a state of grace cannot receive Holy Communion at a Catholic Mass.
It is out of charity that the Catholic Church does not allow non-Catholics from non-Apostolic faiths to receive Holy Communion. They would be condemning themselves since many of them do not believe that the Eucharist is truly the Body, Blood, Soul and Divinity of Jesus Christ which is what the Catholic Church believes and teaches.
Why would one who doesn't believe what the Church believes want to receive Holy Communion at a Catholic Mass?
Those who belong to the Lord belong at His Table. Those who do not belong to the Lord do not belong at His Table. There really isn't any more to it. Whose Table is at the focal point of a Roman Catholic church?
I'm not suggesting that the Vatican announce a blanket welcome of all baptized believers to the altar (as you say, there is no such blanket welcome for Catholics). I am suggesting that priests be allowed extreme discretion when it comes to dealing with Christians of other denominations.
We're all on the same team, are we not?