There’s an old joke about some athlete (a golfer, I think) who was described as Scottish when he started out. Then, as he won more and more games, he became English, then British, until he lost when he became the lad from (golfer’s home town).
This was presented as the quirk of a particular sports announcer. It had a kind of resurgence back when it looked like Andy Murray might win the finals at Wimbledon. (a few years ago, now)
Are you sure you’re not thinking of Ben Johnson? When he won the Olympics he was Canadian in the Canadian press; when he was exposed as a drug cheat he was a Jamaican.
Can’t help you with the joke, but pretty much any talented New Zealander finds that they are readily claimed as actually being ‘Australia’s very own …’ the moment they achieve something. Just ask Australia’s very own Russell Crowe or Neil Finn.
Bennett Cerf told this story. I know it isn’t the joke, but it has similar elements about achievement = acceptance (with a second theme of the oppressed become the oppressor):
There was an African gentleman, a citizen of the British Commonwealth, who immigrated to England in the 1950s. He found employment as a butler, and prospered. But his one ambition was to get a fine suit made by a first-class English tailor.
To that end, he saved his money up for months and months, and finally went to the tailor’s shop on Saville Row. There he picked out the material, and the tailor fitted him and went to work. After many visits, the finished suit was ready.
The gentleman stood in front of the mirror in his fine new suit.
And burst into tears.
The tailor was crestfallen. “Please sir, tell me what’s wrong, and I’ll make it right immediately!”
The gentleman replied, "No, no. The suit is fine. But why did we have to lose India?!"
I’m also reminded of Einstein’s prediction that if his theories turned out to be correct, the Germans would say he was German, and the French would say he was a citizen of the world. If incorrect, the Germans would say he was Jewish, and the French would say he was German.
Why is the sequence Scottish, English, British?
God loves New Zealand, he gave us boiling mud,
God’s the full quid, 'cause that isn’t all he did,
God gave us rugby, you can’t kick boiling mud.
God loves New Zealand, he gave us boiling mud,
God’s the full quid, 'cause that isn’t all he did,
God gave us sheep, you can’t sleep with boiling mud.
God loves New Zealand, he gave us boiling mud,
God’s the full quid, 'cause that isn’t all he did,
God gave us cricket, you can’t lose at boiling mud.
God loves New Zealand, he gave us boiling mud,
God’s the full quid, 'cause that isn’t all he did,
God gave us Australia, you can’t live in boiling mud.
Just to clarify as well, the Andy Murray suggestion was utter bollocks. It never happened. Merely confirmation bias by people with an agenda already whereas the actual stats do not back it up.
I don’t know that I have ever heard anyone claim either of the Finns as Aussies. In the case of Russell Crowe it is because, although he is a New Zealand citizen still, he has mostly lived here since he was 4.
As to the OP I recall many years ago a Melbourne Cup winner attracted headlines like “Queensland Owned Horse Wins Cup,” in Queensland, “NSW Jockey Rides Cup Winner,” in NSW and “Victorian Horse Wins Cup,” in Victoria where it was trained.
What is true, however, is that Andy Murray is British when he wins but when he tells Euan to steal a torn piece of old cloth, he’s Nicaraguan.
And also, he’s British when he wins, but when he makes a can, he’s Mexican.
That said, he’s British when he wins, but when he doesn’t recall who sang “Two Turntables and a Microphone”, he’s Uzbeck.
Nor should we forget that while he’s British when he wins, when he’s rocking more, he’s Moroccan.
Australian Corner
(After The Big Monty Python Papperbok)
*Australia’s a lovely land!
It’s full of bonza blokes,
Sheilas, beer, and no one’s qu**r,
except in Pommie jokes.
Australians are lovely chaps,
they’re God’s own chosen race,
and if they see a f**ry Pom
they’ll smash him in the face.
Australians like dressing up
in skirts and having fun,
and that’s all we were doing
when the Vice Squad came along.*
“This here’s the wattle, the emblem of our land!
You can stick it in a bottle, or you can hold it in your hand!”
I can’t answer the question about the golfer, but I do know the joke about the Scotsman who didn’t understand the difference between “will” and “shall,” and fell into the Thames while visiting London:
*“I will drown!” he cried. “No one shall save me!”
So nobody tried.** 
*Okay. It may be a lame joke to you, but to a grammarian it’s hilarious! 
It reminds me of the old joke about Hollywood and the stages of an actor’s career:
In a similar style:
The Austrians are brilliant people. They made the world believe that Hitler was a German and Beethoven an Austrian.
Prior to the American Revolution, a prominent and influential fellow from Philadelphia traveled to England to speak to the members of Parliament, as certain taxes and amongst other impositions placed on the Colonies were causing unrest, and he sought to intercede.
He was rebuffed, a provincial Subject had no business telling England what to do.
Benjamin Franklin went to Parliament an Englishman, and returned an American.
Q: If you are Russian beforehand and Finnish afterwards, what are you in between?
A: European
Reminds me of a hot divorcee with whom I once spent a long weekend… :o
I’ve heard it told as a joke about Tiger Woods (I think by a black comedian): When he was just starting off, he was a black golfer. Then he started winning tournaments, and was biracial. By the time he was the best in the world, he was a quarter black. Until finally, the headlines were “black golfer in sex scandal”.
Now then. a thread about perceptions of ethnic origin and Tiger Woods turns up - I was sure it was going to be this:
(First 35 seconds).Nothing to do with the OP. Sorry.
j
most likely because I can barely remember the story.
As the golfer keeps winning games, this announcer keeps calling him by a wider nationality (so more and more people can claim their guy won), until the golfer loses the big tournament when the announcer just called him something like ‘John Smith from (some small town in Scotland)’
“But ye fuck one goat…