Sure, lots of references taken out of context, including the alternating singing, which almost always refers to singing the Psalms and not the Mass per se. As I said, little bits of information are taken (usually out of context) by those with an agenda and woven together into a narrative. Just be careful taking the "findings" of various scholars as fact, simply because they take some quote from a Father or the "Middle Ages" out of context. I see this nonsense being done dishonestly ALL THE TIME. I myself require seeing the full context before drawing a conclusion, because it's easy to be deceived by people who have an agenda.
We need to be clear about WHAT people are singing and in what context and when, etc. ... before making some claim that there's some categorical God-given mandate for singing.
In fact, various Antiquarianists also try to make these same types of claims about Communion in the Hand where they make assertions that it was widespread in the "early Church" based on a combination of flimsy evidence, assumptions, and an agenda.
And of course, over time, the Holy Ghost in some areas may have improved the Church's discipline, as St. Thomas points out and so does Pius XII in Mediator Dei, where the Pope explains that just because something is found in some allegedly "older" text doesn't mean it's a better or somehow "more pure" discipline and that the current one used by the Church isn't better.
There was some use of "altar girls" even in parts of the Church early on, and we know this because a Pope had to explicitly condemn the practice. Even the "early Church" was not immune to abuses and aberrations, nor were the Middle Ages, etc. ... especially since groups were more isolated. Heck, even today, where communication is great, I've been in various chapels where the Liturgy is rather a mess and their practices have become rather non-standard and aberrant. What would be the case back in the day when groups were even more isolated due to poorer communication and the expensiveness of written books.
But some "scholar" could find some isolated reference to an altar girl in use somewhere ... where it could have been an aberration ... and then extrapolate from that (based on their wishful thinking) that this was a widespread practice and somehow approved of by the Church overall in antiquity ... as I said, finding a fragment of information without full context, adding some fallacious assumptions, and then weaving it into some narrative consistent with whatever agenda they might have.
And, by the way, I see this kind of practice commonly even outside matters related to the Faith, in just secular historical matters, where in that case the underlying agenda for presenting speculation as scholarship and theory as fact happens to be some "scholar" trying to make a name of himself. Heck, we see it all the time in modern science also, where someone takes a tiny bit of information, formulates a theory consistent with those facts, and then presents the theory as if it were proven fact, rather than just as a possibly-viable hypothesis not inconsistent with the currently-known facts. And, yet, most of these hypotheses-presented-as-fact end up being falsifed and invalidated, replaced by the new "truths" within a very short period of time. Yet people take the new one as "Gospel truth" even though it contradicts the previous one that was held with equal certainty.