Kutuzov was ordered by Tsar Alexander to give up the high ground at Austerlitz and perform an utterly ridiculous maneuver that involved splitting up the forces in the South into 4 columns and sweeping northwards, which Napoleon promptly took advantage of by securing the high ground, and defeating the columns in detail. However, let's look at the sequence of the War of the Third Coalition.
As I understood the chronology, Kutuzov and the Russians were approaching Ulm to reinforce the Austrians there fighting the French. However, Napoleon encircles and forces Mack of Austria to surrender before the Russian Army arrives, and then Kutuzov (heading the reinforcement army), realized he has roughly 50,000 troops against a French force that outnumbered him massively. He then conducted a retreat against an overwhelming French force approaching Vienna, initially in the same direction so Napoleon's approach towards Vienna was also chasing Kutuzov. When Mortier's corp was located on the opposite side of a river from the main French force, Kutuzov sent troops to counterattack this relatively smaller French force, and then moved northwards.
Confusion afterwards penetrated the French command, because they had been both chasing the Russians and moving towards Vienna. Some of the marshals decided to continue the attack on Vienna instead of pursuing the Russian army, much to Napoleon's consternation (he berated them for rushing to Vienna and acting like children). In the end, the Russian Army escapes to be a part of Austerlitz. By using the position of the rivers and adept generalship, the Russians escape a force commanded by Napoleon, one of the greatest generals of Western history, that outnumbered them 4:1, roughly (I don't have the book to reference the exact numbers). I call that a worthy achievement.
This is the second retreat that I mentioned. I admittedly do not know as much of the first retreat because Kagan's book only covered the diplomacy and the War of the Third Coalition in detail, not before. Now that I am looking at the battles, I may be unintentionally attributing Suvarov's success to Kutuzov.
The actual battle of Austerlitz is an example of something that would have worked with better communications and radios (in the modern era) and not with the structures of the day. The allied army was split in the South and North, and then was split even further in the South into four different marching columns. Kutuzov never agreed with the battle plan, and tried to delay marching off the high ground (he was in charge of one of the Southern columns) because he realized it was a tactical error. However, Tsar Alexander personally overruled him and ordered him to march. It wasn't his decision to make.
Birdjaguar, I'm also not pushing for Borodino to be added, just saying that both of the commanders had their high points (particularly Kutuzov, whom I think is underrated as a commander). In my original statement which you quoted, I said it was more of a simple battle of attrition and not known for its clever maneuvers.