When I lived in Hawaii that was a different environment (90% humidity and 300 inches of rain a year) and many shooters would put oil down bores and then spray a boresnake with carb or brake cleaner and pull it through before shooting. I watched blued steel rust overnight if you forgot to wipe it down and stainless would follow suit if you waited a few days.
Now I typically clean with wipeout or patch out, push a dry patch through to finish and put nothing but bullets down it until it starts to shoot bad. I just cleaned a .270 down to bare steel after several hundred rounds so I could look at the throat. First round out at 200 yards landed in the middle of the group from a "dry barrel".
As smokepole mentioned I would be leery of anyone promoting 4 strokes of a brush for every round fired unless he owned a barrel shop and wanted to push sales.
Hunt hard, kill clean, waste nothing and offer no apologies.
"In rifle work, group size is of some interest...but it is well to remember that a rifleman does not shoot groups, he shoots shots." Jeff Cooper
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