An applicant for a permit to dredge from an area which is or may be subject to tidal inundation claimed as the private property of the applicant must provide the department with sufficient proof of such ownership; and this proof shall be accompanied by a recent survey plat indicating the exact location of such area, or the department will presume the ownership of such area is vested in the state. In all such instances, the applicant has the burden to satisfy the department concerning the question of ownership, and the department reserves the right to demand adequate proof of ownership prior to granting a permit for such area. The attorney general shall be requested to examine the title to all claims of private ownership, and those findings shall be taken as final on questions of title.