A few things:
1) HMS Victory is not a commissioned naval ship, she isn't technically even afloat. USS Constitution is not only afloat, she is carried on the books as a active ship in the US Navy.
2) Sadly that whole story about the water and taking on of spirits is all made up.
a) "Her mission: "To destroy and harass English shipping"
Well, on 27 July 1798, the US and the Kingdom of Great Britain were at peace. The Revolution ended 15 years earlier and the War of 1812 was 14 years in the future. Actually, we were in a "Quasi-war" with France at the time.
b) "Making Jamaica on 6 October,... "
Official records state the USS Constitution sailed from Boston on the evening of July 22, 1798*, with orders to cruise between Cape Henry, Virginia, and Charleston, South Carolina. On October 6, the ship was at Hampton Roads, Virginia, very far away from Jamaica. (Jamaica, by the way, was the headquarters of the British West India squadron, a strange place to steer for if one were at war with them).
c) "Then she headed for the Azores , arriving there 12 November...."
Again history records a less interesting November, on the 12th the USS Constitution lay at anchor in Boston Harbor, having just returned from a largely uninteresting first cruise.
d) "On 18 November, she set sail for England . . . In the ensuing days she defeated five British men-of-war ships, and captured and scuttled 12 English merchant ships, salvaging only the rum aboard each."
Well, on the 18th of November, the Constitution was still in Boston...but she did sail for the Caribbean after Christmas. On January 26, 1799, she was heading for Prince Rupert’s Bay, Dominica, to repair the injured foremast–not launching a foray into the Firth of Clyde. On February 20, Captain Nicholson and his crew were patrolling the waters off Guadeloupe.
c) "She carried no evaporators (i.e. fresh water distillers)."
Here's a big problem. At this time in history, evaporators were part of the ship's stove, and the British certainly had them as part of their Brodie stoves. And since Constitution‘s first galley stove came from England, it is entirely possible that it was outfitted with a condenser.
d) " . . . and 79,400 gallons of rum."
In 1799, a Navy Department estimate of provisions for a 44-gun frigate included 8,650 gallons of rum (at a dollar per gallon).
In 1814, Captain Charles Stewart testimony in a court of inquiry included a list of all the provisions taken on board USS Constitution for a six month cruise. These “load out” figures were: 9,546 gallons of spirits and 47,265 gallons of water.
At a dollar a gallon the price of the story's rum provisions are about a third of the cost the ship herself.
e) "On July 27, 1798, the U.S.S. Constitution sailed from Boston with a full complement of 475 officers and men..."
In fact, the muster rolls for the first cruise are missing, so, we don’t know the exact number of people this ship had on board when she sailed in 1798 – however, according to the Naval Armament Act of 1797, a 44-gun frigate was authorized to carry 359 officers and men**, a plus-up of 116 men seems a bit extreme.
1 - Captain
4 - Lieutenants
1 – Chaplain
1 – Surgeon
2 – Surgeon’s Mates
1 Sailing Master, 1 Purser, 1 Boatswain, 1 Gunner, 1 Sail-maker, 1 Carpenter, 8 Midshipmen,
2 Master’s Mates, 1 Clerk, 2 Boatswain’s Mates, 1 Coxswain, 1 Sailmaker’s Mate, 2 Gunner’s Mates, 1 Yeoman, 11 Quarter Gunners, 2 Carpenter’s Mates, 1 Armorer, 1 Steward, 1 Cooper, 1 Master-at-Arms, 1 Cook
150 Able Seamen
103 Ordinary Seamen
1 - Lieutenant of Marines
1 – Sergeant
1 – Corporal
1 – Fife
1 – Drum
50 - Marines
* This was her maiden voyage, by the way.
** An Act to Provide Naval Armament, 27 March 1794, Third Congress, Session I