For honesty's sake...the quote is very suspect and I have grave reservations about it.
I have been unable to find any writings by William Rosecrans where he says these words about Rogers. Rosecrans does mention him by name in his official report, but only to say he led the final charge against Battery Robinett. Years later he wrote an article for Century Magazine and here he stated Rogers had been shot down by a drummer boy. (Insert eyeroll here).
The quote comes from Confederate Veteran Magazine (1907) and a letter written 36 years after the battle by 1st Lt. John Crane, adjutant of the 17th Wisconsin Infantry. The letter is to a woman he had met in New York and promised more details of the battle. He gives a very stirring account of the battle, which, sadly, do not agree with the historic record or are downright impossible.
He told her the 17th Wisconsin of McArthur's brigade "was placed in a position to defend Battery Robinett." Actually, the 17th Wisconsin was on the extreme Union left flank and on the south side of the Corona Female Academy. There were two other forts, Phillips and Williams, between his position and Battery Robinett. He may have been able to see the fighting if he climbed to the top of the brick college, as the college was located on high ground, but as it was 1/2 a mile away, the details might have been hard to make out. If he stayed with his regiment he could not have been able to see the fighting at all as they were on the reverse slope of the hill.
He told her how Rogers approached the fort on horseback (true) and that he jumped the ditch and the wall (false). The ditch in front of Battery Robinett was 15 feet across at the top and 3 feet deep. Most accounts have the ditch filled with dead and wounded before the third attack had been spent. On the far side of the ditch is a narrow step, 10 to 12 inches wide and then the wall rises at an angle of 60 degrees to a height of just over 6 feet. The full height of the rampart was 7 feet and the walls were 15 feet thick. "Before he (Rogers) had realized it he had jumped his horse across the ditch in front of the guns, and was in the midst of us." That would have been a whopper of a leap. Besides clearing the wall, for the horse to land in the "midst" of the 17th Wisconsin would have required the beast to fly like Pegasus.
There are several "eyewitness" accounts of Rogers riding his horse to the top of the wall with the flag in one hand, a pistol in the other, and his sword in his third hand. I would invite anyone who thinks he made it to the top of the wall, mounted or otherwise, to read the very graphic accounts of Lt. Charles Labuzan and Pvt. William McKinstry of the 42nd Alabama Infantry. They make it abundantly clear such an action was simply simply impossible.
"We laid the body of Colonel Rogers reverently in the shade and covered him with an overcoat. When the battle was ended, General Rosecrans came over and asked us to uncover the face. He said 'He was one of the bravest men that ever led a charge. Bury him with military honors and mark his grave, so his friends can claim him.'"
And there is the source of the quote. If anyone else heard Rosecrans it was not recorded. I think it is a great quote and certainly its deserving. I just believe that the man who said it was a Lt. from Wisconsin, and not Maj. General Rosecrans.
And concerning his being buried with honors. I've never found a letter, diary, report, etc about anyone being given a special burial following the battle. In fact, I can't find anything about burial parties, and believed me I've looked (It's my job afterall).