First of all, the 21-centimeter line is "cold enough" so that its presence is universally connected with cold hydrogen, namely with interstellar gas.
This spectral line may appear both as emission and as absorption. We see emission lines from the interstellar gas if there is no source behind the interstellar gas; we may also see absorption lines if there is a source of all frequencies behind the interstellar gas. In the latter case, the interstellar gas' absorption exceeds its emission. This is the dominant process in the case of the Cas-A spectrum on the image so (2) is basically correct.
Otherwise the lines' frequencies are not sharply determined in the graph. In the context of astrophysics, virtually all deviations from the "precisely right frequency" of the 21-centimeter line are due to the Doppler shift i.e. the relative motion of the interstellar gas with respect to us. The graph mostly shows absorption and one may calculate the radial speeds of the clouds that are reducing the function in the graph in this way (from the frequencies).
The explanation (1) contains almost no component of the truth because Cas A is a remnant of a type IIb supernova that exploded a few centuries ago (more precisely, that's when the light describing the explosion reached the Earth). Such supernova remnants have virtually no hydrogen in the shells – because even the star that led to this explosion, probably a red giant, had already have just the helium core and almost no hydrogen envelope.
So pretty much all the spectral features of the hydrogen have to be due to the interstellar gas.
It is not true that the emission and absorption always cancels. Once again, emission dominates when the interstellar gas is "warmer" at the given frequency than the environment behind it; absorption wins when the source behind the interstellar gas is "warmer" at the frequency (literally think about the intensity as if it were temperature and realize that the heat goes from a warmer body to a cooler one).