There are actually three different processes referred to as 'bluing.'
'Rust' bluing IS a oxidative process, in which the solution is applied, the parts (usually the double bbls. of a db shotgun, as hot bluing melts the solder holding the bbls. together) put in a moist environment overnight, and the reddish rust carefully removed. This process is repeated several times.
The most common form of bluing is the 'hot method.' This is not truly an oxidative process (IIRC; others with contradictory or clarifying information please feel free to correct me). It is the familiar finish found on almost all current firearms.
'Cold bluing' is the familiar stuff you dab on metal to color it. It is not an oxidative process either (IIRC; see above).
The rust prevention of all forms of bluing is virtually nil. Cold bluing is the worst, with the other two just barely better.
So, use your Tuf-Cloth, regular or Marine, to protect your bluing; don't expect the bluing to protect itself.
Hope this helps. Comments, questions, and criticisms gladly accepted. Walt