Purity is a method-dependent figure, and that is not a limitation of the measurement, it is a property of what the measurement actually answers.
Temperature affects the dynamics of molecular conformation, and if a peptide has proline residues that interconvert on the chromatographic timescale, the peak will split or shoulder at low temperature and collapse at high temperature.
Put another way, mass on column affects detector linearity and peak overlap — overloading broadens peaks and hides neighbours, while underloading improves resolution but loses sensitivity.
Inter-laboratory studies on identical peptide material routinely find half-a-per-cent to a full-per-cent spreads in reported purity on the same sample.
The limitation is that single-digit micro-impurities become invisible at typical reporting thresholds, so "no impurities detected" means "none above one in two thousand."
Compare purity within a single laboratory on the same method, never across laboratories.