I am not trying to start WWWIII either, so don't take it personal. To me a transcription is when someone takes information from an original or primary source, and re-writes it on another record.
So, a census index would be a transcription. A primary source would be one that is close to the source, I.e. a birth record would count, because the parents would report the name and it was created at the time of the event. Now, if someone re -wrote that info in another database or index, that would be a transcription, or you could call it a secondary source. If there was a delayed birth certificate filed years after the birth, that information would also be more prone to errors. I am not saying all birth records are error free. So the short answer is, a document created at the time of the event can be a primary source. When someone copies it, unless it is a photocopy, then it is a transcription.
I think I over reacted to the original posters remark, that surely Elza's Mother intended to name her something else. Now, I have lots of questions I would like to ask my ancestors, but I don't think they will be answering me! Now, if all he had was census records, that would be one thing. Since he had already seen the birth record, he knew she had been named Elza. I understand his curiosity about where the name might have come from, since it is not very common.