Belfast is right about the chronology of 1960s versions of this song. Dave Van Ronk tells the story in his recent (posthumous) book "Mayor of MacDougall Street":

Dylan was recording his first album when he ran into Dave and asked if it was OK for him to cut a rendition of Dave's arrangement of the song. Dave responded that he wished he wouldn't, since he planned to record it himself soon. Bob starts stammering and getting all evasive, then admits that he had already recorded the song earlier that day. That seems to have been the beginning or the end of the two men's friendship.

For a few years afterwords, DVR would constantly be irritated when audiences would refer to his vocal and guitar performance/arrangement as "that Dylan song." Another couple of years later, though, he enjoyed a sort of revenge when The Bob had to endure a similar experience as the public identified his cover of "Rising Sun" as "that Animals song."

Minor thread drift: A fairly recent development, surprising to me, was the Blind Boys of Alabama's recording of the lyrics to "Amazing Grace" to the familiar "House of the Rising Sun" melody as sung by Dave, Bob, and Eric Burden.

Further drift: jeffp, glad to hear that the tumor was a dying one.