What counts as an outcome of a grant?
The rule of thumb that I generally use is that if any portion of a work has been supported by a particular grant, then it counts as part of the outcomes of that grant.  

Typically, in reporting on outcomes, one is asked not just for names of papers, but also for some sort of narrative of the work, in which it is simple to state what work was done, much as you just did.  If for some odd reason the funding agency only wants you to list papers and nothing else, then I would think that it is incumbent upon them to understand that they may not be the sole source of support for some of the items listed.