It does make sense. "Begging the question" is a term of art from philosophy meaning to assume the thing you set out to prove--e.g. God exists because the Bible says so, and the Bible must be right because it is the literal word of God.
This shift towards using the phrase to mean "raise the question" makes it harder for a writer to tag a claim as being guilty of that particular logical fallacy.
But your first point is right: language changes, and we have to accept new usages, even bad ones.