Not only is the quote not true, it's not even close to being true in 1814.
At the time not only was the War of 1812 going on but also the Napoleonic Wars in Europe meant that European fleet strengths were at their highest (in purely numeric terms) levels in history.
According to Jean Sutton's Lords of the East, between 1791 and 1832 the East India Company had around 450 ships in service (excluding warships). However, most of these were in service for only part of that time, so the actual number in service in 1812-15 was probably nearer 100-150. The East India Company's warships never amounted to more than a dozen or so vessels at any one time (and most of them were frigate sized or smaller).
In comparison, the British Navy's fleet in the same period was nearly a thousand ships of all sizes. So just on that comparison alone, the East India Company is only about a fifth the size of the British Navy. If you add in the substantial French, Russian, Spanish, Dutch, Ottoman, US and Scandinavian fleets and the East India Company comes no where near to having " more ships than the combined fleets of all the nations of the world".
Lords of the East, Jean Sutton (Conway, 1981)
British Warships in the Age of Sail, 1793-1817, Rif Winfield (Seaforth, 2005)