My understanding of the Prime Directive is that it applies to directly interacting with developing civilizations. If Starfleet can act to save a world or civilization with a reasonably high level of confidence that they can do so without making their presence known to that civilization, then they will. The goal is to avoid contaminating the natural development of cultures (and probably also to avoid providing potentially destructive technologies to species that have not had the time to develop socially far enough to handle them without getting a lot of people killed), not to be selfish dillweeds.
I think the reason Picard initially refused Data's request was Drema IV was not advanced enough to be beyond PD concerns, but was
sufficiently advanced to have a reasonable chance of realizing that an outside influence had done something if they acted.