"Back in the day" - when aural/oral tradition was the only way to record and preserve a song - I suspect that in some cultures there was a great importance placed on learning & repeating the song exactly. At least amongst those people who were entrusted with the task of preserving knowledge (Bards, skaalds, Christian monks, etc).
Certainly the folk process was also at work cultures (or other segments of the same cultures), and there were a lot of entertainers (troubedors, minstrels, etc.) who regularly changed lyrics to match the current circumstances. For example, an itinerant singer might well alter a "standard" song to praise his current patron. The next month, as a guest at a different household, he might change it yet again to include the host's name & deeds.
Now in our age of printed music & lyrics and sound recordings, both of these traditions are fading. We do not have the same cultural need for performers to preserve our heritage - that's done by computers these days. So there is not as much emphasis placed on learning a folk song note-for-note and word-for-word. By the same token, a recording of a song can become widespread and thus becomes thought of as the "right" way to perform it - and anyone who changes it is "doing it wrong".
There's also the whole ugly issue of copyright and how much you need to change an arrangement of a public domain song to avoid infringing upon someone else's money - but I think that issue has been hashed out in other threads.
As for me personally, I'm of the camp that you need to internalize a song & make it your own in terms of arrangement - as long as you're a soloist. Just realize that significant changes to melody and/or lyrics may throw other people off.