Normally I sing a ballad, or ballad fragment, just the way I heard it. Or even leave our one or two verses that don't add anything in particular. As Ewan McColl leaves out the verse in Thomas Rymer about wading through rivers of blood.
Many American versions of the Child ballads are only ballad fragments. They are good fragments; sing them as they are. I for sure would not go borrow verses from a Scots version and try and paste them in, because they would sound artificial. If the audience knows the story, they can live with gaps. IMO, the question is not whether what you sing tells the entire story, but whether the song would gain or lose force if verses were added/omitted.
Often they gain something if not all the story is told. For example if the ballad is about a criminal (e.g. Young Hunting) we don't really need a lot of detail about how the criminal is punished. Some of the most bloody ballads just become unbearable if all the verses are sung; examples are McColl's versions of Lamkin and Sir Hugh and the Jew's Daughter. Those are extremely good versions, and I guess you should sing all the verses, if you sing them at all. I couldn't.
And not all ballads are worth singing all the way through. My favorite version of Old Bangum is still the Burl Ives version, which leaves out almost all the story. It has a haunting effect the long-winded version simply lacks.