I feel sure that there was more honour to be had by defeating an opponent through seamanship and gunnery skills than through a ‘lucky strike’ with an ‘infernal weapon’, and thus there may have been an incentive to suppress information.
But I wouldn’t necessarily expect to find information in official reports and logs. Ship’s logs typically include very little detail of the guns and weapons used in an action. The gunner would of course have to account for shot and powder used, but presumably not for anything provided privately by the captain.
In this case Coleridge’s account says that the lieutenant used the combustibles without Ball’s knowledge, and thus without Nelson’s knowledge. But there is an interesting comparison at the Battle of Copenhagen. There the 56-gun
Glatton, Captain Bligh, (anchored next in line to Nelson in the
Elephant) fired incendiary ‘carcasses’ at the Danish flagship
Dannebrog and set her on fire within the first hour of the battle. The Danish Commander Fischer transferred his flag to another ship and the
Dannebrog blew up several hours later. Most of the crew had by then been taken off by British and Danish boats, but that was only made possible by the truce. Bligh continued firing incendiary shells during the battle and Nelson must have been aware of this, but as far as I am aware, did not issues any orders for Bligh to desist.
In fact, while making his offer of a truce, Nelson threatened to set fire to the captured floating batteries, explicitly pointing out that while the action continued, he had no means of taking off the Danish seamen before he did so. Perhaps fortunately for Nelson’s legend, during the time it took for his message to be delivered, the Danish resistance crumbled and his offer of truce was accepted.
There is no reason to doubt Nelson’s humanity, but the time for humanity was after victory, and not before.
Let me indulge in some wild speculation for a moment (which is what the Internet is for, isn’t it?

). It would be consistent with Nelson’s battle tactics for him to want to strike at the enemy command and control by ‘taking out’ the enemy commander-in-chief. Suppose he had quietly told his captains to use all means available to destroy the enemy’s flagship. If that was the case, I think it likely that information about his instructions would have been subsequently suppressed. I’m not suggesting that is what happened, just that we probably wouldn’t know if it had.