This does not directly answer the question, but gives the details of the story, including the source of the error.

*Time Magazine, Monday April 30, 1945:*

_{ The year is erroneously given as 1943 in the book linked to below}

A sure way for any mathematician to achieve immortal fame would be to
prove or disprove the Riemann hypothesis. This baffling theory, which
deals with prime numbers, is usually stated in Riemann's symbolism as
follows: "All the nontrivial zeros of the zeta function of *s*, a
complex variable, lie on the line where $\sigma$ is ½ -- ($\sigma$
being the real part of *s*)." The theory was propounded in 1859 by
Georg Friedrich Bernhard Riemann (who revolutionized geometry and laid
the foundations for Einstein's theory of relativity). No layman has
ever been able to understand it and no mathematician has ever proved
it.

One day last month electrifying news arrived at the University of
Chicago office of Dr. Adrian A. Albert, editor of the Transactions of
the American Mathematical Society. A wire from the society's
secretary, University of Pennsylvania Professor John R. Kline, asked
Editor Albert to stop the presses: a paper disproving the Riemann
hypothesis was on the way. Its author: Professor Hans Adolf
Rademacher, a refugee German mathematician now at Penn.

On the heels of the telegram came a letter from Professor Rademacher
himself, reporting that his calculations had been checked and
confirmed by famed Mathematician Carl Siegel of Princeton's Institute
for Advanced Study. Editor Albert got ready to publish the historic
paper in the May issue. U.S. mathematicians, hearing the wildfire
rumor, held their breath. Alas for drama, last week the issue went to
press without the Rademacher article. At the last moment the professor
wired meekly that it was all a mistake; on rechecking. Mathematician
Siegel had discovered a flaw (undisclosed) in the Rademacher
reasoning. U.S. mathematicians felt much like the morning after a
phony armistice celebration. Sighed Editor Albert: ''The whole thing
certainly raised a lot of false hopes."

The "undisclosed" flaw found by Siegel is identified on page 109 of The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics:

Rademacher was terribly embarrased by the ordeal and never spoke of it again. [...] It was well known that no one was to mention the words "Riemann hypothesis" in his presence.So I would imagine any copies of this withdrawn manuscript would have been well hidden, the AMS perhaps still has a copy in their files... $\endgroup$ – Carlo Beenakker Feb 21 '18 at 16:50false[my emphasis], and then do this, this, and this, and you get a contradiction, then it must be true." So based on that, the conclusion would have been RH is true. In other words, based on the description that you quoted, it sounds as if Rademacher was trying to prove RH is true, via a proof by contradiction. Not a disproof by contradiction. $\endgroup$ – Todd Trimble♦ Nov 17 '18 at 14:37