No, you have to go with the flow and make the song work, especially if your a hired gun and not a permanent member.
I used to play (occasionally) with a lead singer that was a little scatterbrained. He would sing verses out of order, so you would just have to lay back and see if the chorus, bridge, or another verse was coming next.
LOL! As a singer who tends to take liberty with cover melodies, I've been there. However, switching a couple verses, verses throwing choruses and bridges in the wrong place are two different things in my opinion. I feel song structure is important to get correctly as some people out there usually are very familiar and that structure is probably what helped the song get traction.
With the melody line...when I'm asked to learn a new song I'll listen to it on repeat for maybe an hr. Then put it away and sing it how it occurs to me. It's funny when sometimes I'll then listen to the song again months later and I'll have been singing it quite differently than it was written. I feel this adds my own spin to it though =)