  We investigate the physical properties of structures seen in channel map
observations of 21-cm neutral hydrogen (HI) emission. HI intensity maps display
prominent linear structures that are well aligned with the ambient magnetic
field in the diffuse interstellar medium (ISM). Some literature hold that these
structures are "velocity caustics", fluctuations imprinted by the turbulent
velocity field, and are not three-dimensional density structures in the ISM. We
test this hypothesis by stacking probes of the density field -- broadband far
infrared (FIR) emission and the integrated HI column density (NHI) -- at the
locations of linear HI intensity structures. We find that the HI intensity
features are real density structures and not velocity caustics. We generalize
the investigation to all small-scale structure in HI channel maps, and analyze
this correlation as a function of velocity channel width, finding no measurable
contribution from velocity caustics to the HI channel map emission. Further, we
find that small-scale HI channel maps structures have elevated FIR/NHI,
implying that this emission originates from a colder, denser phase of the ISM
than the surrounding material. The data are consistent with a multi-phase
diffuse ISM in which small-scale structures in narrow HI channel maps are
preferentially cold neutral medium (CNM) that is anisotropically distributed
and aligned with the local magnetic field. The shallow spatial power spectrum
(SPS) of narrow HI channels is often attributed to velocity caustics. We
conjecture instead that the small-scale structure and narrow linewidths typical
of CNM explain the observed relationship between the SPS and channel width.
