That was fun and interesting. I don't own a Quad and only drove one for a quick trip around the block, so I can't comment on the validity.
They watered down, and championed the green four leaf clover. From what I can remember, the driver crashed a lot, he did well when he didn't crash, but crashed a lot. His team-mates put the clover on his car telling him it was for good luck, "Now you won't crash." He won that race without crashing. The symbol was put on all of his cars after that and he did well. Then he took out a car without the clover, crashed and died. His team-mates put the green four leaf clover on their cars as a way of honoring their fallen team-mate.
The version in the video, although very simplified, is the correct one.
Ugo Sivocci was one of the "four musketeers" - so they were called - of the Alfa Romeo racing team. The other 3 drivers were Antonio Ascari, Giuseppe Campari, and Enzo Ferrari.
Sivocci was a very good driver and did very well, but he was very unlucky and victory always escaped him. He seemed to be destined to be an "eternal second". At the 1923 Targa Florio, he decided to paint cloverleaves on the hood of his RL Targa Florio, inscribed in a square.
And he won in the most rocambolesque way.
It's the last lap. Sivocci is running second, Antonio Ascari is leading the race.
But disaster strikes. Ascari's car breaks down on the final stretch! The mechanics run to his car, and work frantically to fix it.
They manage to get it running again. The mechanics all hop onto Ascari's car in celebration, and cross the finish line. Ascari's still first, such was his lead.
The race judges take exception with the mechanic-mobile. Ascari has to go back to where the car broke down, and repeat the final stretch alone.
By then, Sivocci catches up, and wins his first ever race (and Alfa's first ever Targa Florio).
The Quadrifoglio worked!
Fast forward about six months. Sivocci's in Monza, preparing for the Grand Prix. He's out testing the then-new P1. Which still doesn't have the cloverleaves on. He crashes and dies.
From that day, all racing Alfas had Sivocci's cloverleaf - except now inscribed in a triangle rather than in a square, the loss of one corner symbolizing the loss of one of the four musketeers.
As a side note: the car in which Sivocci won the 1923 Targa Florio had racing number 13. The P1 in which he died had number 17. In Italy, 13 is considered a lucky number, and 17 an unlucky one.
Also, Sivocci introduced Enzo Ferrari to the automotive world. After WW1, Ferrari was unemployed, flat out broke, and desperate, even contemplating suicide at one point. He befriended Sivocci, who often took him as his guest in his home, and supported him. Sivocci then found Enzo his first auto job, as a test driver for CMN, where he also worked.