When you say sunk, your column implies it was sunk by a notified sub, though it seems that the sub lay some mines, one of which Kitchener’s ship struck–perhaps the mines were laid down sometime in advance, or was that also perhaps prompted by the alleged notification?
Here’s a link to the column in question: Did loose lips actually sink any ships? - The Straight Dope
Cecil Adams says ‘True or not’. It could be that Duquesne embellished the story, or that he believed that his notification caused the sinking even if it didn’t. In any case, it wasn’t an instance of careless talk being overheard by the wrong ears. If Duquesne’s story is true, it is a case of a spy passing on first-hand knowledge.
I think the phrase ‘Loose lips sink ships’ isn’t supposed to be taken literally. Instead it is an admonishment to not speak carelessly, since bits of data taken in aggregate amount to ‘intelligence’ that can be used to the enemy’s advantage. And it scans better than ‘Loose lips can adversely affect the outcome of the war.’
Yay, first post for me! 
While I agree with his main point about the value of pieces of information gained through evesdropping, I think Cecil’s blog post over emphasized the UK, which really wasn’t an issue for the most part due to the overwhelming effectiveness of Double Cross: Double-Cross System - Wikipedia
To be fair that was the origin of the poster in question, if memory serves, but I’d suggest looking at activities in other countries for better examples.
Duquesne was a good start to support the point but as was pointed out in the post above, that’s really more dependent on who you ask.
Of course in the end I guess the only thing that’s really true about intelligence information gathering from overheard information is that it’s only as truthful as the person who’s saying it can be, or however it can be twisted to support whatever the person overhearing it wants it to be. 
There are a few problems with your suggestion though:
[ol][li]While as far as I can tell the phrase was from WWII (or at least popularized then), the concern was from WWI, which many of Cecil’s examples referenced.[]The Double Cross system, while it was an incredibly successful feat of counter-intelligence, was not widely-known among the general public. The authorities could hardly say, “Well, don’t bother worrying about what you say, we’ve got all the baddies already.”[]Even officials did not know how complete the Double-Cross system was until after the war. During the war, there was the possibility that one or two German agents had escaped the dragnet.[]Seeing as how the phrase was primarily one used on American propaganda posters, saying that Cecil should be looking elsewhere besides the UK is curious. All of the discussion of the Dusquene spy ring was looking at the US experience.[]Dusquene’s claims of actually sinking the HMS Hampshire in WWI may be dubious, but his actual attempts to pass information across the ocean in WWII are not. Those efforts depended almost entirely on overheard information of the type that the slogan warned against. Furthermore, he likely did sink a few freighters in WWII using time-bombs he planted while working as a rubber agent in Brazil.[/li][/ol]
Be careful not to confuse the actions that Cecil discussed in the two wars.