The link is not entirely untrue, but it is false that “the first Thanksgiving” occurred in 1637. As @jonsblond noted, the first Thanksgiving really did occur soon after the Pilgrims landed in 1620.
It’s true that the Pilgrims landed on what was essentially deserted (not “uninhabited”) land, because they found evidence of corn planting, storage and other cultivation, and recent habitation, but few residents. The Native tribes had already experienced smallpox and their numbers had been reduced by as much as 50–70% (if I recall correctly from my reading). That’s because although the Pilgrims were the first European settlers in that part of the world, they were not the first Europeans to have spent time there. Prior to the Mayflower landing at what is now Plymouth, Massachusetts, Portuguese and other fishermen had landed there from time to time after becoming shipwrecked, blown off course and separated from their fleets and mother ships, and doing some exploring. (The reason that the Pilgrims could communicate with the Natives was because Squanto had spent time in the company of English sailors and had picked up the language.) Some sailors had overwintered on the coast until they could repair their ships and boats and put to sea in spring again to rejoin the fishing fleets. Various relations and trading interactions with Native peoples were had…
Although smallpox became a form of biological warfare later, the smallpox epidemic that made Cape Cod so empty for the Pilgrims was entirely accidental and normal for the way epidemics spread through unprotected people.
So the Pilgrims actually aided the Natives a bit, too, as well as being helped through their first winter in New England.
As the Native populations rebounded in later years, there were cultural differences with the Pilgrims and Puritans who followed. Those developed into what is now known (and more or less un-known to us moderns) as King Phillip’s War. The end of the war, with the Native populations reduced by more than 90% and all of the adult men sold into slavery in the Caribbean is decidedly brutal, to be sure.
But that’s not a reason to abrogate the spirit of the first Thanksgiving.
I recommend the book Mayflower by Nathaniel Philbrick if you’d like to know more about this period in American (European-American, anyway) history.