Therefore, consequences relating to the teaching of the Church are not to be inferred from these occurrences.
Parse.
The "teaching of the church" has never been in question in this affair.
The question is both pastoral and practical. Even Kasper says that the "teaching of the Church" should remain the same. It's exceptions to that teaching which are the issue. Are there pastoral situations in which divorced and remarried Catholics may receive Communion? And is this one such situation?
Specifically, did the Pope provide such advice to this woman?
The pastoral response would be to seek a way to bring those living in sin to return to following the will of God, not making them comfortable in their sins.
Your question is important of course, but if I may say it’s importance is only insomuch as it may indicate bad pastoral care on the part of Pope Francis. And that’s all we (as Catholics) should be concerned about really. IOW, Pope Francis isn’t any more of a threat to the teaching authority of the Church any more than any other “bad Pope” through the centuries. Indeed, if this is the worst we may suffer, we’re pretty well off.
I tend to agree with FR. Z’s take on the issue. The woman probably heard the Pope say, “Divorced people are free to take communion” (which has always been true) and tuned out the rest, specifically when he (probably) said something like “Divorced people can receive but not those who also remarry”.
Then again, maybe he didn’t add the second sentence above and thus, again, that would be poor pastoral care on his part. But not in any way a danger to Church dogma.
Stories like this are largely only useful to those who hate the Church. Either spurned “traditionalists” who demand their own version of doctrinal purity or scorned anti-Catholics who use this as another “justification” of their assertion of the fallible nature of Popes throughout the centuries. Neither of which is proof of anything of course except in their own minds.
So we shouldn’t give it any more weight than it deserves. Which is very little.