Possibly the show's writers have been reading social history or ethnography. According to Stephanie Koontz in Marriage, a History (2006),
Eskimo couples often had cospousal arrangements, in which each partner
had sexual relations with the other's spouse.
The book itself has more details about the practice, including, if I recall correctly, notes on the relative absence of jealousy, but is not the only source of this information.
The practice (or more properly, practices, since particular forms vary depending on the peoples and also within cultures) has been discussed by anthropologists since at least the 1960s, with somewhat sensationalized reports of the custom back to the 1800s:
Among the Eskimo around Bering Strait, "It is a common custom for two
men living in different villages to agree to become bond-fellows or
brothers by adoption. Having made this arrangement, whenever one of
the two men goes to the other's village he is received as the bond
brother's guest and is given the use of his host's bed with his wife
during his stay." (Nelson, 1896-97, p. 292). (Quoted in Rubel, link below.)
"Eskimo wife-sharing" has been a "rumor" in some form since at least the early 2000s, as this 2003 "Straight Dope" question and answer attests, and thus could have been known, at least in broad outline, by your high school friends when you first heard the term.
It doesn't seem like a very big stretch to generalize from a vague understanding of these practices, combining reports of "blood brothers" and the more familiar term "sister wives", to come up with "Eskimo Brothers".
As requested, some additional references (note that these aren't necessarily the most pivotal articles, just some that are available without a subscription):
Arthur J. Rubel, "Partnership and Wife-Exchange Among the Eskimo and Aleut of Northern North America" (1961)
ARTHUR J. RuBEL
Lawrence Hennigh, "Functions and Limitations of Alaskan Eskimo Wife Trading", (1970)
Johnnetta B. Cole, Anthropology for the Nineties: Introductory Readings, "Marriage Among the North Alaskan Eskimos" (1988)
Kathrine E. Starkweather and Raymond Hames, "A Survey of Non-Classical Polyandry" (2012)