You are asking a question to which there is no answer.
The chariot was a frequent image in the old 19th and early 20th century spirituals; some of the songs are related and some are not (of course, no authors are known). The Fisk Jubilee Singers were just one of the early groups that sang the song (their choral organization goes back to the 1870s; that of the Hampton Institute started almost as early and they are only the two best known of the early groups singing spirituals). Both groups sang "Swing Low Sweet Chariot" in the 1870s. The Fisk recording date of 1910 thus is not useful since the song was sung by their touring group and other groups long before that.

Many singers have recorded their own versions of these songs. The Cleveland Index does not list a "Swing Down..." in their list of spirituals; it may be fairly recent. It is listed as traditional at this website, but many of these sites have incorrect attributions: Swing Down
I have not heard the Elvis version. Are there any recorded comments by him about the song and the origin of his copyrighted version? He came from a Delta background, and he probably heard several different versions of Swing Low... during his early years. Where did he hear "Swing Down..."?

A number of gospel and art versions that are identified with a singer or a group, but identifying the primary source of their particular version is difficult if not impossible. Did they get it from their church? Versions sung by different congregations could vary widely. Did they synthesize it from other versions, either from books or other singers?

Seems incongruous to hear that these spiritual songs would be sung at rugby matches.