I suspect that the basis of this is true, particularly as the De Soto was an actual Union Navy vessel.

However, I can not find any record of the De Soto capturing any ships other than blockade runners.

De Soto, Steamer: Capt. G.H. Scott, Capt. W.M. Walker, and Lt. Commander R.F. Bradford. Mate John R. Neeld.

There was a U.S.S. Stonewall that was a tender to the U.S.S. Tahoma and U.S.S. Pursuit (at Tampa).

There was a C.S.S. Stonewall that was an ironclad ram.

At one time, the De Soto was assigned to cruise for the C.S.S. Oreto and the C.S.S. Alabama. No indication that it found them.

Captures:
Jane Allie, sloop out of Mobile. August 16, 1863
Bright, sloop out of Mobile. August 16, 1863
Alice Vivian, steamer from Mobile
James Battle, steamer from Mobile. July 18, 1863
Adelie, Schooners. April 24, 1863
Barataria Bay, Louisiana.
Clarita, Schooner. April 26, 1863
Cuba, Confederate steamer. May 17, 1863. Burned
Cumberland, British sidewheel iron steamer. Feb. 5, 1864
General Prim, Schooner. April 24, 1863
Rapid, Schooner. April 24, 1863
Lady Maria, Schooner. July 6, 1863
Leviathan, Steamer. September 22, 1863
Major Barbour, Schooner. January 28, 1862
Mississippian, Schooner. May 19, 1863
Montgomery, Steamer. September 13, 1863
Nita, Steamer. August 17, 1863
Sea Bird, Schooner. May 13, 1863
Star, Schooner. February 8, 1862
William Bagley, schooner from Mobile. July 18, 1863. Lost claim to capture.

There may be more, these are just all that I have found. The De Soto routinely took its prizes to Key West, which angered other Captains, who thought that the prizes should properly have gone to New Orleans. This too fits with the story of the fishing boat being used out of Key West following the war.

On June 9, 1864, the U.S.S. DeSoto was ordered north to N.H. from Key West for sanitization.