(a) No license as a transporter shall be required of any of the following:
(1) Banks, trust companies, building and loan associations, organized under the laws of this State or authorized to do business in this State while transporting their own property;
(2) Incorporated telegraph companies insofar as they receive money at any of their respective offices or agencies for immediate transmission by telegraph.
(b) Nothing contained in this section or in any other section of this chapter shall be construed to enlarge or limit the rights which any of the above-named organizations have under any existing law.