  We present a comprehensive theory of the dynamics and fluctuations of a
two-dimensional suspension of polar active particles in an incompressible fluid
confined to a substrate. We show that, depending on the sign of a single
parameter, a state with polar orientational order is anomalously stable (or
anomalously unstable), with a nonzero relaxation (or growth) rate for angular
fluctuations at zero wavenumber. This screening of the broken-symmetry mode in
the stable state does lead to conventional rather than giant number
fluctuations as argued by Bricard et al., Nature ${\bf 503}$, 95 (2013), but
their bend instability in a splay-stable flock does not exist and the polar
phase has long-range order in two dimensions. Our theory also describes
confined three-dimensional thin-film suspensions of active polar particles as
well as dense compressible active polar rods, and predicts a flocking
transition without a banding instability
