I remember one time where I was traveling to Bali. Showed airline staff my confirmation on phone but she wanted to see it on paper. Luckily by chance, I had it on paper but I normally don't. I think it's always better to be safe than sorry.
I'll chime in that this question comes up often and it's so different for each person because as we know, T.I.T and what one immi officer says is ok or not can be totally different from another.
I personally ran into MANY problems when I finished my contract and my prev employer didn't cancel anything. Supposedly they were told that since I finished my contract, nothing else needs to be done. They were so wrong!