I write tunes and I am very suspicious of this "the tune just popped into my head" notion. In my experience creating a tune that is complete is very rare. More often what you get is a basic musical idea that needs to be worked up. Sometimes I can complete a tune fairly quickly, but often I worry at it for weeks, even months or year before I am satisfied.

Other times I store a musical fragment away until I find some way of completing it or using it.

I think Edison's description of invention applies just as much to composing 5% inspiration, 95% perspiration.

I also see nothing wrong in using an existing melody to fit your words if that is what works for your song. It is an approach that has a long an honourable history. Most Broadside ballad writers specified an existing tune for their songs. Even the Star of County Down is acceptable as far as I am concerned <g>