First, volunteer wheat is volunteer wheat.  Makes no difference if first growth, second growth, regrowth, whatever it all is potential disease problem for planted wheat.

Now the fun part, the neighbor that does nothing to his volunteer wheat.  I have asked him point blank when he plans on taking care of the volunteer.  Sometimes it helps, most of the time not, so I try to plant resistant varieties in those fields.  Did have one neighbor, who after being affected 2 years in a row, went into the neighbors field and worked it up.  No words were ever exchanged, and like talking to him, it worked for a couple of years, then it was back to letting it go.

Just no real answer, but I would keep after him every year.  Maybe he will get tired enough of hearing about it to where he will just let you spray it yourself if you want.  Of course, don't expect monetary compensation.