In general I don't think this is an issue with the better labs. Certainly, Janoshik can identify peptides from blind samples with HPLC-MS. Otherwise, they wouldn't be able to tell you what it really is (eg MOTS-C vs Tirz) in a screwup. What they can't really do is tell you purity of different components, if there are multiple components, because all of the peak overlap each other, but they can still give weight of each one, if each is known. I'm not an expert in these particular measurements, but I've used HPLC.
The other problem is reconstitution. It's possible to get peptides that won't dissolve properly (eg at a particular pH) and that can lead to ZERO peptide results. This happened recently with Survo that appeared to be free base (or incorrect salt) which would dissolve at lower pH.
Of course NN and EL apparently ship freebase (non salt) in their pens with whatever bacteriostatic/preservative necessary to get months of room temp storage. They don't need to do any lyophilization.
Now, if you're talking about things bigger than peptides (proteins), then folding becomes an issue for "biologics" and chemically they can be the same, but one folding could be effective while the other is not. Stereo isomers (or racemic mixtures) are another issue for small molecules, but again apparently not an issue in the solid phase synthesis used for the common peptides.
Again, I'm not an expert in these particular measurements, but the explanations I've read by others make sense from a chemical manfuacturing, purification, storage, and testing perspective.