Usually, when logging companies go about logging, they also clear the underbrush, in some cases, its actually part of the agreement (i.e. you can log, but you also have to do this).
In other cases, they clear out trees before they turn. During last summers, little "brushfires across the land" (stupid cnn) even the enviornmentalists were admitting that you may have to make agreements with loggers to clear the brush, and that they would want to clear some of the healty trees to. However there objection was that then the loggers would be profitting from a civic responsibility and the government should just do it itself.
recycling takes away any motivations for loggers to log in the first place, so they aren't going to clear the brush either.