UPDATE: See the text of "Mr. Parkman's Tour" here.
Melville did write this, we know for sure. The manuscript copy in Melville's handwriting has survived and is now in the Duyckinck Collection, Manuscripts and Archives Division, The New York Public Library.
For the only modern printing of "Mr. Parkman's Tour" you have to get hold of the Northwestern-Newberry Edition of Melville's The Piazza Tales and Other Prose Pieces, 1839-1860.
For the original printing you have to find volume 4 of the New York Literary World and look for the March 31, 1849 issue. Melville's anonymous review of Parkman's California and Oregon Trail appears on pages 291-293. Google Books has the right digitized 1849 Literary World 4, but the dang thing lacks the pages with Melville's original article.
Our own intrepid sleuths have managed after much trouble and incalculable expense to dig up serviceable (we hope) scans of the elusive pages with Melville's known review--known, but perhaps not as well known as it deserves. Some people (that would be Norman E. Hoyle and yours truly) think Melville probably reviewed other books of western travel and adventure for the Literary World during the same period, such as the unsigned review of J. Quinn Thornton's Oregon and California in 1848 titled "The Western Trail."
Mr. Parkman's Tour 1
Literary World (March 31, 1849): 291
|"Mr Parkman's Tour" part 1|
NY Literary World 4 (March 31, 1849): 291
Mr. Parkman's Tour 2
Literary World (March 31, 1849): 292
|"Mr Parkman's Tour" part 2|
NY Literary World 4 (March 31, 1849): 292
Mr. Parkman's Tour 3
Literary World (March 31, 1849): 293
|"Mr Parkman's Tour" part 3|
NY Literary World 4 (March 31, 1849): 293