Brownings are known -- rightly or not -- for having rust-prone chambers.
When you shoot a gun to the point of being hot, then leave it in the range rack on a cold day, water can condense, especially in the chamber. This has happened to me with various kinds of guns, not just Brownings, but for some reason, it's axiomatic that you should wipe the chambers of a Browning with RemOil, Sheath, Rusthunter, or somesuch, before casing the thing.
Perhaps Browning wants to overcome this reputation (I can't say whether it's justified).
AFAIK barrels tend to be chromed, including the chamber. One reason a clay gun might not be would be that people like to have the insides of their barrels modified (forcing cone lengthening, backboring, etc.). That's easier to do with a plain steel barrel, and there's no expectation that the gunsmith will re-chrome it if it's not chromed to begin with.
All told, I wouldn't sweat it. And your hunting gun is probably chromed anyway, if it's recent.