I'd blame NASA for using the word "reservoir".
And even if this hypothetical layperson doesn't know how far a light-year is, 12 billion certainly gets across the point that it is an awful lot of them.
I am not a PR person myself, but I think the vast majority of laypeople who stumble across the headline "large, distant reservoir" would assume that the source is tappable. They might also ignore or not really understand the issue of the 12 billion light years -- or the inconvenience, to say the least, of the quasar nearby.