The story is that he was asked by the late Mr Lee Kuan Yew to join the Singapore Airlines (SIA) board to iron out tensions between management and unions which were then running high.
More than 12 years later, SIA chairman Stephen Lee squashes this urban legend.
The request had in fact come through the board, he told The Sunday Times in a rare interview, though he can understand why the myth has lived on.
Back then, the late Mr Lee was concerned that the internal problems at SIA would affect the airline's ability to compete effectively in an increasingly tough operating landscape.
Tensions were high between the airline's top brass and pilots' union. Unhappy with layoffs and pay cuts in the wake of the Sars crisis, which had crippled the air travel industry, the pilots ousted their union heads in 2003 and threatened to strike.
Determined to set them straight, Mr Lee summoned all parties to the Istana and warned both pilots and management that if they "play this game, there are going to be broken heads".
Mr Stephen Lee was then president of the Singapore National Employers Federation (SNEF) - a seat he held for 26 years until he stepped down in 2014 - and PSA chairman.
Just before the SIA saga, PSA had also undergone a major restructuring in late 2003, which involved axing jobs amid tough times. The late Mr Lee cited it as an example of how a crisis could be handled without dispute.
"Perhaps it was Mr Lee's personal involvement that led to the belief (that he had asked me to join the board)," said Mr Stephen Lee, referring to the many discussions that Singapore's founding Prime Minister had with SIA's top brass and unions then.
Of the four unions that represent SIA workers, ties with the pilots' union - the only major union in Singapore not affiliated to the National Trades Union Congress - have historically been the most contentious.
While he refuses to take credit, Mr Stephen Lee is widely credited with improving management-union ties at SIA. More than a decade after hitting rock bottom, relations are now less acrimonious and more constructive, he said.
"Back then, the relationship was more contentious and discussions centred more around bargaining instead of problem-solving. Communication channels then were not as wide or open, and management and unions usually met during structured meetings."
Today, discussions are more frequent and open, and while worker welfare remains the top priority for union leaders, the thinking has changed, he added. This is due in part to increasing awareness that SIA faces serious competition both from full-service premium airlines and low-cost carriers.
Union leaders continue to look after the welfare of their members "but perhaps with longer-term and more sustainable benefits in mind rather than fighting for short-term gains", Mr Lee explained.
On its part, the management is now more willing to share future plans so that the unions are more informed, he added.
Mr Lee said: "It has been satisfying....working directly with the ground and with the union leaders."