It appears to me that it is not necessary that the dependent variable would come from count data. Please see the [source one][1] and [source two][2], which give examples of studies that have used fractional regression with fractional dependent variables that are based on various types of data.

  [1]: https://www.stata.com/meeting/mexico16/slides/Mexico16_Dorta.pdf
  [2]: https://www.stata.com/stata14/fractional-outcome-models/