Benignant,
Cleaning it with the method you discovered sounds like it will certainly get it clean. But the point is that it may get it cleaner than necessary, or even cleaner than optimum. Browned surfaces are slightly porous. Leaving some rust in those pores is much like filling the pores of a walnut stock. The rusted surface holds oil and prevents the gun from rusting further. If you clean the browned surface too much, you may end up with a matt surface. In contrast, Dave is suggesting a smooth surface, which, as I said, has the pores filled. But you could experiment and see what you like best. You may like the matt surface better.