Henry Villard, referenced above, is a primary source. He wrote of his own personal interaction with Rosecrans. Another primary source mentioning the Cincinnati Commercial newspaper and W.D.B (this is Bickham) is the regimental history of the 7th Illinois. Rosecrans and Bickham insulted the 2nd Division at Corinth even though they bore the brunt of two days of fighting.
Here is an excerpt from the regimental history:
Tuesday, 14th. — This morning our camp is staked off, and we take our position and stake our tents. Our brigade now consists of the Seventh, Fiftieth and Fifty-seventh Illinois, and the Twenty-second and Eighty-first Ohio, commanded by Colonel A. J. Babcock, of the Seventh. There is a commotion in the Second Division. The Cincinnati Commercial, with W. D. B.'s lying communication, vilifying and basely misrepresenting the heroic Second Division, who so bravely stemmed the current of battle on Corinth's sanguinary field, has been circulated. The heroes of Belmont, Fort Donelson and Shiloh rage to-night, and adding still more to this correspondent's vilification, comes the congratulatory address of General Rosecrans, with the following remarkable passage .. " I desire especially to offer my thanks to General Davies and his Division, whose magnificent fighting on the third more than atones for all that was lacking on the fourth." As a defense, we will simply transcribe the circular of "Justice," written by a soldier of the Second Division, which gives a clear exposition of facts relative to the history of the Second Division in the two day's battle at Corinth ..
" They did fail to do what they should have done, namely ..
there were captured by the whole army of Rosecrans, two thousand two hundred and sixty-eight prisoners, and the Second Division (Davies'), captured only one thousand four hundred and sixty of that number, mostly on the fourth; they should have captured the whole.
Then again the whole army captured fourteen stand of colors; Davies' Division captured ten of these on the fourth ; they should have taken all!
They fought Van Dorn and Price's army on the third, alone, and whipped them. This was right. On the fourth they fought with others and whipped the enemy ; they should have done it alone and would have done so but for the giving may of troops on the right flank — names I will not mention.
Now, the Second Division well know they should have done all these things alone, and they must throw themselves upon the clemency of a for giving country. The throbbing patriot's heart will have some sympathy, and the facts will atone for the short-comings of the Second Division when they are told that they went into action on the third with two thousand nine hundred and twenty-five officers and men, the balance of the Division being detailed in and about Corinth. Loss, seventy-five officers; total loss, one thousand and four. Forgive these " lacking and erring boys of the Northwest, for next time they will try and do better."