Answer: You're right the second time. The minor key signature refers only to what is found in the "natural minor." If you raise a seventh at some point, or a 7th and a 6th, those require accidentals. Somewhere else in one of these answers I may have said that I don't think any composer sets out to write a piece in "harmonic minor, " or "melodic minor." It's just more common to vary degrees in minor than it is in major, whether for harmonic or melodic reasons, and the ones most often varied are the 7th and the 6th degrees.

Imagine a D minor piece, key signature of one flat, in which you want to raise the C to make a strong cadence back to D. That would be "harmonic minor" and would require a sharp on the C, but there is no standard key signature that would include both sharps and flats. You can find experimental signatures that do include both sharps and flats, but the trouble with such experiments is always that so many musicians exist who are used to the standard method and find the experimental ones hard to learn. So we're likely to stick with traditional signatures, or no signatures, plus accidentals.