I read the article you have linked here; the author really does a poor job of citing any sources for this instance. He cites "an account, written by a cavalryman of the Virginia infantry," but doesn't list the title of the account or who wrote it. Also, saying someone was a "cavalryman" in the infantry is confusing.

So, I went searching. It turns out, the account he cites is the book One of Jackson's Foot Cavalry: His Experience and what He Saw During the War 1861-1865 : Including a History of "F Company," Richmond, Va., 21st Regiment Virginia Infantry, Second Brigade, Jackson's Division, Second Corps, A.N. Va, by John H. Worsham. The full text is free through Google Books, and I've included the link here. The title explains author of the article's misstatement of a cavalryman in the infantry; "Stonewall" Jackson's infantry brigade was nicknamed "foot cavalry" due to how fast they covered ground, not because they rode horses.

Worsham does write an account of the fistfight you refer to. He writes he was an eyewitness to the event. He writes,

"We were then treated to a rare sight! Running midway across the little field was a gully that had been washed by the rains. In their retreat, many of the enemy went into this gully for protection from our fire, and when we advanced to it, we ordered them out and to the rear; all came out except one, who had hidden under an overhanging bank, and was overlooked. When we fell back across the field the Yankees, who followed us to the edge of the woods, shot at us as we crossed. One of our men, thinking the fire too warm, dropped into the gully for protection. It will be noticed that there were then a Yankee and a Confederate in the gully, and each was ignorant of the presence of the other! After a while the commenced to move about in the gully, there being no danger as long as they did not show themselves. Soon they came in view of each other, and commenced to banter one another. Then they decided that they would go into the road and have a regular fist and skull fight, the best man to have the other as his prisoner. When the two men came into the road about midway between the lines of battle, in full view of both sides around the field, one a Yankee, the other "a Johnny," while both sides were firing, they surely created a commotion! This was true in our line and I suppose in the enemy's line, because both sides ceased firing! When the two men took off their coats and commenced to fight with their fists, a yell went up along each line, and men rushed to the edge of the opening for a better view! The "Johnny" soon at the "Yank" down, who surrendered, and both quietly rolled into the gully, where they remained until night, when "the Johnny" brought "the Yank" into our line. The disappearance of the two men was the signal for the resumption of firing! Such is war!" (Worsham 1912, 203-204).

At any rate, this is the source the article pulled from. It seems pretty legit. It's a primary source, written by an eyewitness. It's also fairly believable; soldiers became accidentally trapped by sudden advances or retreats during the Civil War on many occasions, and you read about this sort of thing happening in other wars too (The First World War had many examples of troops being stranded when they took cover in a shell hole, and were overrun by an enemy advance). This is also the sort of thing that would grab the memory of an enlisted man in the line of battle, but may not reach the notice of the commander writing the "official" report later on, which may explain why it doesn't appear in the Official Records (Disclaimer: I did a very cursory look, and the OR is MASSIVE). His description of the battlefield tracks with the actual battlefield as well.

At any rate, it's plausible. Certainly dramatic. Hope this helps!