Is the story true?

[Gene C]

That makes sense to me considering Stanton's reaction to Sherman's terms and condition for Johnson' surrender at the end of the war. 
Stanton took  Sherman as overstepping his authority

"Sherman believed that the terms that he had agreed to were consistent with the views that Lincoln had expressed at City Point, and that they offered the best way to prevent Johnston from ordering his men to go into the wilderness and conduct a destructive guerrilla campaign. However, Sherman had proceeded without authority from Grant, the newly installed President Andrew Johnson, or the Cabinet. The assassination of Lincoln had caused the political climate in Washington to turn against the prospect of a rapid reconciliation with the defeated Confederates, and the Johnson administration rejected Sherman's terms. Grant may have had to intervene to save Sherman from dismissal for having overstepped his authority.[162] The U.S. Secretary of War, Edwin M. Stanton, leaked Sherman's memorandum to The New York Times, intimating that Sherman might have been bribed to allow Davis to escape capture by the Union troops.[163] This precipitated a deep and long-lasting enmity between Sherman and Stanton, and it intensified Sherman's disdain for politicians."
(Wikipedia)