Did Scott report the results of his investigation to the Cabinet? Or to Lincoln? Or to the press?
How do we know them? Post-war memoirs?
Given the war and the political situation, how would Lincoln or Stanton publicly apologize? After all, they couldn't just bring the subject up at a televised press conference.
Supply SNAFUs are not uncommon in the military even today. I doubt that any recent administration- particularly a war-time administration- in a similar situation would publicly discuss them.
So to answer these questions:
1) Did Scott report the results of his investigation to the Cabinet? Or to Lincoln? Or to the press?
Lincoln, Halleck and Stanton.
The clamor over supplies caught Lincoln's attention, and he sent Col. Thomas A. Scott, former assistant secretary of war, on a fact-finding mission to evaluate McClellan's complaints firsthand at his headquarters near Harpers Ferry. "About the middle of October 1862," he recalled, "I had a conversation with Mr. Stanton, Secretary of War, and President Lincoln, in regard to the delay in the movement of General McClellan's army, and its reported condition of inefficiency to effect a movement without proper and greatly needed supplies." McClellan told Scott the matter did not require discussion—he would have one of his staff "show me the requisitions . . . for supplies, and also a statement of the amount received, and that I could draw my own inferences."
Scott verified a shortage of "shoes, clothing, and other necessaries for the men." Satisfied, Scott returned to Washington and reported his findings to Lincoln, Halleck, and Stanton:
Both Mr. Stanton and General Halleck then repeated their assurances that all General McClellan's requisitions had been met; and it was suggested that, as the troops in the forts around Washington constituted a part of the Army of the Potomac, the supplies that were intended for General McClellan's army in the field, instead of having been sent to him at Harper's Ferry, had by some means or other [emphasis added] been diverted for use of the troops in the fortifications, and thus had failed to reach him. This proved to be the explanation of the trouble.
Stotelmyer, Steven R.. Too Useful to Sacrifice: Reconsidering George B. McClellan's Generalship in the Maryland Campaign from South Mountain to Antietam (pp. 250-251). Savas Beatie. Kindle Edition.
2) How do we know them?
A letter of Scott's in 1880, though Stotlemyer identified several cases of corroborating evidence. Indeed, the evidence for there being a supply crisis is pretty overwhelming - my favourite is
18th October: McClellan complains about how he's not getting the clothes he asked for
18th October: Halleck (General in Chief) asks Meigs (the quartermaster general) about this
18th-25th October: special wagon trains ship about 50,000 pairs of boots and shoes to the Army of the Potomac
25th October: Meigs reports back "Yeah, there's no problem, the Army of the Potomac has loads of shoes, on the 20th and 21st they got tens of thousands of shoes"
So the proof there was no crisis is that Meigs put in huge effort to solve the problem
after being pressed and then used the fact the problem
had been solved as evidence it didn't exist in the first place.
3) How would Lincoln or Stanton publicly apologize?
Presumably by the same means that McClellan was accused,
including after Scott's report. The
New York Tribune's front banner headline on October 24 (days after Scott reported) was
No Foundation for the Complaint!
I would argue that there were certainly means to publicly apologize, but even if you're not doing that then the least you can do is to not
continue making the accusations...
Of course, not firing McClellan would have gone a long way, given that one of the reasons Lincoln gave for the firing was
the delay - the same delay which Scott's report indicated was partly due to the supply problems.
4) Supply SNAFUs are common and not publicly discussed
Yes, but it's hardly honest to publicly say
there isn't one and that means that the general who hasn't been advancing must have no reason for not advancing, when in fact his reason is... the supply SNAFU. Simply not publicly discussing it doesn't mean it wasn't true.