For anything in the solar system to be YOUNGER than the sun, it would have to be MADE by the sun, or as a byproduct of the sun achieving fusion. Our planet is younger than the sun itself, but the elements that comprise it are much, much older.
That only applies to atoms, not molecules. I can point to oodles of molecules that in a "most recent step" sense were made by the sun (e.g., through UV radiation or 'solar bleaching') and oodles of molecules that in that same sense were not (e.g., plastics).
TFA is referring to molecules of water and whether they tended to form during planetary disk formation and consolidation:
[Shielding from cosmic radiation] makes it quite hard for these regions in the disk to synthesize any new molecules. This was an 'aha' moment for us -- without any new water creation the only place these ices could have come from was the chemically rich interstellar gas out of which the solar system formed originally."
There is still active debate over when and where the typical water molecule arose in the course of events leading to the formation of water-bearing planets. See this article, for example. If verified, this theory tends to favor interstellar formation.