The Lonnie Donegan story is exaggerated.
The first recordings were issued by the Library of Congress in 1934-1937. "Sing Out!" printed lyrics in 1952.
Donnegan recorded on Decca in 1956 and the record was an influential hit in the UK and North America.
Leadbelly had recorded "Rock Island Line" in 1937 (unissued at the time), but by 1944, four recordings were released. It had been collected by Lomax in 1934. Leadbelly, as a driver for Lomax, heard the song at Cummins State Farm, sung by Kelly Pace and other convicts.
Along with Donegan, the worksong was sung by the Weavers, Odetta, Grandpa Jones, the Tarriers, etc., etc.

Donegan, like the other performers who sang "Rock Island Line," was entitled to profit from his copyright recording. It is still available on UK imports, "King of Skiffle," and "Rock Island Line."
True or not, the tale of Asch and the agent is a common one; agents are always looking for more income- that's their job; but this is not the same as saying that Lonnie Donegan claimed original authorship. Recording companies, moreover, sometimes cited the performer as composer when they should have said 'arranger and performer.' Certainly Donnegan's take was original in its form. Claims by agents or recording companies are only that, and are ignored by anyone who knows the history of the music.

See "The Rock Island Line," pp. 472-477, Norm Cohen, "Long Steel Rail." on which these comments are based.

Others of the examples given by Fred McCormick need amplification and should not be taken at 'face value; I am sure that others will provide critical details as they have time.