Danbo,
I wouldn't use it; I'd be afraid of getting a metallic taste in the cheese.
As you have discovered, stainless steel is not actually impervious to rust; it is just highly resistant. The key is that the chromium/nickel in the mix form an oxide layer that inhibits rusting. However, at least two things can cause rust to occur anyway: 1) Cleaning stainless with a plain-steel wire brush can embed small particles of steel, which will rust ... and once they rust, they open the gateway for the "stainless" to rust as well. 2) Welding on stainless can cause a localized area that does not have the oxidation protection; this can be "passivated" with an acid wash, which I think washes away the excess iron.
I've also found that any sort of scrape, scratch, or pit in stainless can be a gateway for rust or other corrosion. And my experience has been that storing brine in stainless puts the stainless to the ultimate test, exposing any and every slight flaw. One time I had some brine in a decent-quality stainless pot, but there was some sort of pinhole defect that began to produce a greenish corrosion. I chose not to take a chance on how safe the result would be ...
After that, I started storing my brine (and brining my cheese) in a glass container -- which would be forbidden for a commercial enterprise, but fine for home use. When I boil my brine to eliminate any nasties, I do use stainless, but I get it out of the stainless as quickly as I can.