Sorry, but that is just plain wrong... to a degree. Hamilton wrote the one that was given (with Washington's changes), but Washington asked Madison to write the very first one. Very little of what Madison wrote ended up in the end piece, though. Still, Madison was asked to write the first one.
[Washington attempted to retire after one term in 1792. With James Madison he even drafted a farewell "Valedictory Address." Instead of delivering it, however, he was persuaded to remain in office a second term. By 1796 Washington insisted upon retiring from public life. He dusted off the Valedictory and sent the draft to Alexander Hamilton to rewrite in a "plain stile." Although historians have debated if it was Madison, Hamilton, or Washington who authored the Farewell Address, the current consensus is that it was a true collaboration. Although the words are Hamilton's, the ideas and the sentiment are all Washington's.
In the Address Washington articulates once more his political philosophy that the continuation of the American experiment depends upon a united virtuous, educated citizenry and a strong central government to hold disparate groups together. To Washington, the rise of partisan politics threatened national unity. Permanent foreign alliances were dangerous because they constricted American interests and dampened independence. Above all, Washington offered himself to the American people as the model of the classically conservative republican: deferential, virtuous, selfless, and responsible to the rule of law as expressed by the Constitution. Washington never delivered his Farewell Address publicly, rather it was circulated in newspapers printed first in the Philadelphia's American Daily Advertiser on September 19, 1796.]
Washington was no isolationist. In fact, although he preferred not to label himself with political parties, he was in fact a Federalist. Neither the Federalists nor the early Republicans were isolationists; the key issue at the time was which side the U.S. should be more in favor of (the French and the British had long been at war). Washington and the rest of the Federalists thought it was within the best interest of the country to be more supportive of Britain, while the Republicans favored the French.
Washington more than likely did not want this issue to divide the country, because he saw it as partisan politics.
Never mind Madison and Washington's Farewell Address.
The 'good' story is that he wrote Washington's Inaugural Address, then
he wrote the House of Representatives' reply to that address, then he wrote
the president's reply to the House of Representatives' reply. And then
for good measure, he wrote the president's reply to the Senate's
response to the inaugural address as well.
http://www.booknotes.org/Transcript/?ProgramID=1290
"...we do know it as a historical fact. We have the drafts of these things." (the author doesn't distinguish between draft and write)
For a while he was Representative 'Prime Minister' Madison!