  The new formalism for description of (un)polarized semi-inclusive DIS at
moderate energies is developed. Hadron production is modeled as a product of
distribution functions and hadronization functions (HFs) weighted by the hard
scattering cross sections, as it is done in the {\tt LEPTO} event generator.
The correct treatment of polarization effects shows that description of
semi-inclusive DIS within this formalism includes a new nonperturbative input
-- {\it polarized} HFs. It is shown that this approach does not correspond to
the commonly adopted one with the independent quark fragmentation. The purity
method used by the HERMES collaboration mixes up the two approaches and ignores
the contributions from polarized HFs. This method cannot be considered a
precise tool for the extraction of polarized quark distributions from measured
SIDIS asymmetries.
