What is the etymology of "Assistant Professor"?
The OP dictionary is inaccurate.  The term assistant professor was in use prior to 1827.  

In the 1805 book The College of Fort William in Bengal there is an article dated 20 September 1804, beginning on page 225, that uses the term several times, to name several assistant professors of various languages.  The term is used in this article at pages 226, 227 and 228, and the book also list four assistant professors on page 237.  

Also, the 1801 The New Universal Biographical Dictionary, and American Remembrancer, volume 4 says, under the entry for James Hay Beattie: 


  On the 4th June, 1787, the king, upon the unanimous recommendation of the university, appointed him assistant professor of moral philosophy and logic, although he was not then nineteen years of age. 


And volume 2 of the same Dictionary, in the entry for Euler says:  


  he was called to St. Petersburgh, and was admitted as an assistant professor in the university of that city ... In 1730, he was promoted to the professorship of natural philosophy; and in 1733 he succeeded his friend D. Bernoulli in the mathematical chair. 


However, there is an earlier (1785) version of the Euler biography that uses the term "joint professor" instead of "assistant professor".  

The 1802 book Travels through Sweden, Finland and Lapland to the North-cape, in the years 1798 and 1799 discusses assistant professors, saying for example concerning University of Abo: 


  In the branch of theology there are six professors, three assistant professors, and three private teachers or magiltri docentes: of law, two professors and two assistant professors : of medicine, three professors and two assistant professors : of philosophy, ten professors and twenty assistant professors: of genteel exercises...


Also, in the US, a law was passed 29 April 1812 concerning the Military Academy (meaning West Point): 


  each of the foregoing professors to have an assistant professor, which assistant professor shall be taken from the most prominent characters of the officers or cadets, and receive the pay and emoluments of captains, and no other pay or emoluments, while performing these duties. 


So, at least according to this US law, the assistant professor was assigned to a particular professor.