Understanding purity requires separating the chemistry from the method from the reporting convention, and the three are not independent.
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.
The underlying point is that sample solvent strength affects peak shape — if you inject in strong solvent on a gradient starting in weak solvent, the solvent peak can distort your main peak or create a false shoulder.
I would be careful about over-reading a single measurement — treat it as a data point, not as ground truth.
If you are ranking vendors, specify a method and have all samples tested at the same place.