Mark HOPKINS was, indeed, born at Henderson, NY, and his parents did move to St. Clair, MI, but his parents were Mark HOPKINS & Anastasia KELLOGG of Great Barrington, MA, then Henderson, NY, then St. Clair, MI — not Edward HOPKINS & Hannah CROW of Virginia, then North Carolina.  The evidence contradicting Edward's connection to Mark is given in the sources on his page:

In a nutshell, Edward was born 1781/2 in Virginia and is in the 1830, 1840 and 1850 censuses of Randolph Co., NC.  In other words, Edward HOPKINS was nowhere near New York or Michigan, while Mark HOPKINS, railroad baron, was unquestionable born in NY.

Of course, even if the above family were connected to Mark HOPKINS, they still wouldn't be connected to Stephen HOPKINS, Mayflower Passenger, because the supposed connection between Mark HOPKINS's immigrant ancestor, John HOPKINS of Cambridge, 1634, and Stephen HOPKINS, Mayflower Passenger, is also bogus (see False and Faked Mayflower Genealogy at Caleb Johnson's web site).  HOPKINS is a common English surname, so connections cannot be assumed based on name, alone.  The fact that the above author alleges the connection further destroys his credibility as a researcher.