You are aware that the Happy Birthday Song has dozens upon dozens of variations (and not just the parody ones), right?
The Happy Birthday Song isn't even the Happy Birthday Song! It's Good Morning To All! Happy Birthday lyrics didn't even make it into print until 1912 and that's not even the version that we use today. That version was first published in 1924 by Robert Coleman. The copyrighted version that even credited the Hill sisters with the melody (from Good Morning to All, in 1893) didn't come around till 1935.
As for peoples' literacy, yes, that's the point. That history is often unreliable. We even have disputes between early _written_ historians writing about the same events and have to compare them and also evaluate whether they were alive at the time of the events and what their sources were. Often we can discount what those people wrote today based on what we've learned from the past.
I said 100 years and I meant it. If you really think about it deeply, it should be obvious. Hell, I don't know who my father is and my own mother couldn't manage to stay consistent between tellings of that story...
You expect a complicated tradition to stay the same for 12000 years? I went to Catholic Church my whole childhood and I couldn't even tell you beat-for-beat what happens at mass if you put a gun to my head.