Read the chromatogram before you read the number, because the number without the trace is not a measurement, it is a claim.
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.
Column pore size affects mass transfer — a 100 Angstrom packing on a 5 kDa peptide restricts diffusion, broadening the peak and potentially hiding small impurities in the shoulders.
Published side-by-side method comparisons show that a two-point difference in purity on the same vial is easily explained by method choice alone.
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."
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.