(e) Motor carriers who transport passengers for any nonprofit educational, religious, or charitable institution, society or corporation, or for any nonprofit literary, or scientific institution, or public institution, society, or corporation, or other organizations with tax exempt status by the federal government pursuant to 26 U.S.C.A. §501(c), including their organizers, sponsors, or promoters shall be exempted from the provisions of this chapter while transporting persons pursuant to an otherwise lawful contract or agreement. The provisions of subsection (d) of Section 37-3-20, as amended, shall not be applicable for that service or transportation except as herein provided. The agreement or contract shall not be declared invalid because it is not in compliance with any tariff, schedule of rates, or contracts prescribed by this chapter and no penalties, fines, assessments, or recovery of charges below any required rates, or waived entirely, shall be recovered from the motor carrier or such passenger. Provided, however, that the Alabama Public Service Commission may require the operators of the motor vehicle to register with the Public Service Commission and the commission may inspect these motor vehicles as it deems necessary for purposes of safety, insurance, and visibility of the name of owner or operator of the vehicle. Any motor carrier who transports any nonprofit group passengers shall file quarterly reports with the Public Service Commission, listing the names and addresses of the nonprofit organization, corporation, institution, or society and the organizers, sponsors, or promoters, if any, together with the date and its published fare, rate, and charges for each group. The report shall be cumulative only for the quarter filing as prescribed by the commission. Any carriage heretofore or hereafter conducted by motor carriers exclusively in their vehicles pursuant to an otherwise lawful agreement shall not be declared invalid because it was not in compliance with any tariff, schedule of rates, or contracts required by this chapter and no penalties, fines, assessments, or recovery of charges in excess of or below any prescribed rates may be levied against or recovered by any shipper or motor carrier as a result of the carriage.