Put another way, understanding purity requires separating the chemistry from the method from the reporting convention, and the three are not independent.
The fraction of your main peak that is actually your target versus isomers, fragments or related sequences is invisible without complementary identity testing.
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.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
Worth noting that method standardisation is poor in the research-grade space compared to pharmaceutical work, so identical-looking methods can produce different results.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.