This is basically true information. The Royal Navy (really like all navies) required that ships look immaculate. Officers believed understood that failure to maintain a shipshape appearance would hurt their careers. What's more, the officers had to purchase the necessary paint, for the Admiralty did not provide enough. If they failed to buy paint and set the crew to work, then they'd inevitably look worse than the ships whose officers did these things, and their careers would suffer.

A good source on this is Admiral Sir Percy Scott, Fifty Years in the Royal Navy (1919). Scott was an advocate of advanced gunnery techniques and regular practice, but he was stymied throughout his career by the institutional emphasis on ships' appearance rather than gunnery performance and the reluctance of officers to devote adequate time to gunnery. Here's an extended quote about the Mediterranean Fleet around 1886, explaining his ship's abandonment of training in a new gunnery technique:

But the innovation was not liked, we were twenty years ahead of the times, and in the end we had to do as others were doing. So we gave up instruction in gunnery, spent money on enamel paint, burnished up every bit of steel on board, and soon got the reputation of being a very smart ship. She was certainly very nice in appearance. The nuts of all the bolts on the aft deck were gilded, the magazine keys were electroplated, and statues of Mercury surmounted the revolver racks. In short, nothing was left undone to insure a good inspection.

In those days it was customary for a Commander to spend half his pay, or more, in buying paint to adorn H.M. ships, and it was the only road to promotion. A ship had to look pretty; prettiness was necessary to promotion, and as the Admiralty did not supply sufficient paint or cleaning material for keeping the ship up to the required standard, the officers had to find the money for buying the necessary housemaiding material. The prettiest ship I have ever seen was the Alexandria. I was informed that £2000 had been spent by the officers on her decoration.

In these circumstances it was no wonder that the guns were not fired if it could be avoided, for the powder then used had a most deleterious effect on the paintwork, and one Commander who had his whole ship enamelled told me that it cost him £100 to repaint her after target practice. Fortunately, target practice could easily be avoided; Admirals seldom asked any questions about it, as their ships were generally the worst offenders.

The Duke of Edinburgh, who was then Commander-in-Chief of the Mediterranean, was an exception to the general rule, and took a great interest in gunnery; but in the conditions then prevailing, absence of competition, no encouragement from the Admiralty, and the general impression in the Fleet that gunnery was of no importance it was impossible to improve matters.

Note that the Duke of Edinburgh mentioned by Scott is Prince Alfred, Queen Victoria's second son. He did not have to play by the same rules as everyone else being both very wealthy and well-connected, so could indulge his interest in gunnery.

In 1902, Scott had an audience with King Edward VII (Alfred's brother), in which he explained the Royal Navy's poor gunnery as follows:

(1) Lack of attention to the subject on the part of the Admiralty, which produced lack of interest in it on the part of the officers and men.

(2) That officers' promotion depended upon the cleanliness of the paint work and not upon the battle-worthiness of the ship.

(3) That the Admirals as a rule took no interest in target practice; their custom was to go on shore when it took place.

(The attitude of many Admirals to gunnery since a ship existed only to hit first, hit hard, and keep on hitting reminds me of a story which is not inappropriate. I once heard of a bluejacket, wounded in the foot, who asked a comrade to carry him to the sick bay. He picked him up and carried him along on his back. On the way a splinter carried away the head of the wounded bluejacket. The rescuer deposited the injured man on the floor of the sick bay. The surprised doctor exclaimed, "What have you brought him here for? he has no head! " "Well," was the astonished reply, "Old Bill was always a liar; he said it was his foot." If the war had come before the gunnery of the Fleet was improved, the nation would have had reason to ask, "What is the good of a Navy which cannot shoot?")

(4) That the Fleet was supplied with such bad gun sights that it was impossible to make good shooting with them; the only ships that had made good shooting had used gun sights of a non-Admiralty pattern.

(5) That there was no competition, and without competition the Englishman would do nothing. I pointed out that, only a few years ago, if a man-of-war got in forty tons of coal an hour it was considered very good, but that since Lord Walter Kerr (the then First Lord of the Admiralty) had introduced competition it had gone up to 200 tons an hour.

(6) That the only reason why the Admiralty wanted the results kept confidential was because they were so bad.

Subsequently there were gunnery competitions, though Scott was not sure they emphasized the correct skills.

Another good book on practically anything to do with the Royal Navy from Trafalgar to Jutland is Andrew Gordon, The Rules of the Game (1996). He collects a few more incidents and (as I recall) makes the connection to rapid fire.