The relevant detail is that high-performance liquid chromatography is a separation technique, not an identification technique, and it answers the question "how much of the detected signal is a single species" not "which species is it."
System suitability checks on replicate injections of a known standard establish whether the method was in control — if the peak area varies by more than two per cent between replicates, something is wrong.
Formic acid is the compromise when you need the mass spectrometer on the same run, but the peak shape penalty is real and easily a tenth of a per cent on purity.
Peptide separation by reverse-phase high-performance liquid chromatography is described in the general chapters of the United States Pharmacopeia, European Pharmacopeia and Japanese Pharmacopeia, and the methods converge on essentially the same principles.
The practical summary: specify the method, run the same method on every sample you compare, and use orthogonal techniques to confirm the result.