  We propose the explanation of a surprisingly small hyperfine frequency shift
in the two-dimensional (2D) atomic hydrogen bound to the surface of superfluid
helium below 0.1 K. Owing to the symmetry considerations, the microwave-induced
triplet-singlet transitions of atomic pairs in the fully spin-polarized sample
are forbidden. The apparent nonzero shift is associated with the
density-dependent wall shift of the hyperfine constant and the pressure shift
due to the presence of H atoms in the hyperfine state $a$ not involved in the
observed $b\to c$ transition. The interaction of adsorbed atoms with one
another effectively decreases the binding energy and, consequently, the wall
shift by the amount proportional to their density. The pressure shift of the
$b\to c$ resonance comes from the fact that the impurity $a$-state atoms
interact differently with the initial $b$-state and final $c$-state atoms and
is also linear in density. The net effect of the two contributions, both
specific for 2D hydrogen, is comparable with the experimental observation. To
our knowledge, this is the first mentioning of the density-dependent wall
shift. We also show that the difference between the triplet and singlet
scattering lengths of H atoms, $a_t-a_s=30(5)$ pm, is exactly twice smaller
than the value reported by Ahokas {\it et al.}, Phys. Rev. Lett. {\bf101},
263003 (2008).
