I don't think the BA is there to keep the peptide from degrading man. It's there to keep cooties from growing in the water.
I didn't go too deep into the details, but
I'll expand since you mentioned it.
You're not wrong, in the sense the alcohol is there to prevent bacterial growth.
Any bacteria that develop would present a potential health hazard, but even if they don't, they'll produce enzymes to break down the peptide proteins and feed on them.
So it's both, to maintain sterility, and prevent degradation of the peptide.
Consider this. A single use GLP med pharma pen is made with Bac water, not water for injection, even though it's produced in a sterile environment, and not subject to multiple piercings like a multi use vial. That's an acknowledgment that the possibility of bacteria growth remains, no matter how sterile the conditions of production. These meds have a 2 year expiration date after reconstitution refridgerated, and 30 days at room temperature, which is a testament to how effective Bac is (there are no other preservatives in the pen).
If you added a sufficient quantity of alcohol to milk, like an Irish Cream, it'll keep the milk from spoiling for years, so that's a clearer case of how it's a "preservative" by preventing dangerous bacteria from growing but also the harmless bacteria that would break down the proteins turning the milk to cheese.