If this is true, how exactly did Hamilton (or those truly responsible) accomplish this?
Whether he did so to spare Washington the embarrassment of a loss or to champion the candidacy of a personal and political ally (or for some other reason entirely), Alexander Hamilton did take some steps to prevent John Adams receiving too many electoral votes in the first presidential election.
Alexander Hamilton feared Adams' northern support would threaten Washington's candidacy. Hamilton approached seven or eight electors (two in Connecticut, two in New Jersey, and three or four from Pennsylvania), and asked them to withhold votes from Adams. Hamilton's actions proved unnecessary when, on election day, all 69 electors voted unanimously for Washington, with Adams receiving only 35 votes.
In the months leading up to the election, Hamilton spoke highly - if not passionately - of Adams, "credit(ing) Adams's indisputable patriotism, his 'sound understanding', and his 'ardent love for the public good'" among other things, and it seemed he strongly preferred Adams for Vice President. Still, his cautious scheming for Washington bruised Adams' ego and paved the way for the rift that would develop between the two in the next decade.
All information and quotations are coming from Ron Chernow's Alexander Hamilton.