Partly it was the fact that, unlike a group of business people or shareholders arriving at a crisis meeting, they were prepared to chat and in colourful language. "How the bloody hell was this state of affairs allowed to happen?" queried the venerable abstract artist and senior Royal Academician, 81- year-old William Gear.
Partly it was that the cream of Britain's art establishment - internationally revered artists, but often unworldly and in many cases well past retirement age - appeared nearly in all cases the wrong people to be making financial decisions about an institution costing pounds 15m a year to run in a market that has never been more competitive in the battle to win both private sponsorship and touring exhibitions.
Then they trooped into their private meeting and it was four hours before they emerged for their official dinner. At the end of the day the RAs decided against selling off any works of art and postponed until February a decision on whether to accept a "moderniser's charter", a plan by the new secretary David Gordon and president Sir Philip Dowson to set up a "review board" that would include wealthy and worldly wise trustees, benefactors and business leaders to advise the Academy's general council on financial matters.
After nigh on 230 years of running their own show it is understandable that the Royal Academicians are loath to give up absolute power without at least a two-month postponement. Their first president, Sir Joshua Reynolds, turning uneasily in his grave, is owed at least that. But accept the moderniser's charter they will. After the catalogue of financial incompetence detailed to them at their private meeting, they know they need hard-nosed professionals to manage the money. And it is unlikely that the former ITV chief executive David Gordon, with a get-out clause in his terms of employment to leave next June if he or his employers are unhappy, would want to stay on if his modernising plans are rejected.
Things can be turned around, he believes. "Let's not make a crisis out of a drama," said David Gordon, and he is right. The Royal Academy's short- term situation isn't so dreadfully serious. A pounds 3m accumulated deficit is not unique for an arts institution, and certainly not irreparable for one that has multi-millionaire trustees, an exemplary Friends organisation with 70,000 members, and the money-spinning Summer Exhibition.
No, the problem for the Royal Academy - and in this respect their present cash problems may have done a service in concentrating the mind - is to re-examine the role of the institution in a rapidly changing art world.
And the change has been rapid. Five years ago the present crisis would have been unthinkable as it basked in the kudos and pounds 1.7m profit of the Monet blockbuster exhibition, with the just boast that, unlike all its major rivals, it had not a penny of government funding for its agenda- setting exhibitions from the maverick but much respected exhibitions organiser Norman Rosenthal, and its glorious roomy yet cosy galleries, where evening social functions followed packed daytime visits from the paying public.
But as some in the institution will now privately admit, Monet may have been psychologically damaging. It made the place complacent and, looking back, it is a while since Rosenthal has really set the art world talking with a Royal Academy exhibition. Other art galleries - particularly the publicly funded ones - are now chasing the same business sponsorship that the Royal Academy used to consider its right as a non-grant receiving institution. The Tate is said to now have 36 fundraisers.
Much fuss has been made about the possibility of the Academy selling off its one great treasure, Michelangelo's sculpture Madonna and Child. But how many people, even among the Friends, let alone the general public, even knew it was there. Poorly displayed, outside the Sackler Galleries, and without direct light, its loss would probably not be greatly noticed among a public who come to see specific temporary exhibitions.
There is another area where the Royal Academy has failed to forge a new role. With its tradition and its membership, it should be the centre for education about the visual arts. Last year at a press conference by David Hockney at the Academy to publicise an exhibition of his drawings, the artist digressed to address an issue in the news at the time, that of a newsreader and her partner being reported to the police for taking pictures of their naked child. Hockney was infuriated by this crude interpretation of delight with the human form. He would be giving a lecture in the new year at the Royal Academy, he promised, on the subject. It never happened. And nor have any others.
Why is there no annual Royal Academy lecture which might provide a voice for key participants in the increasingly frenetic debate in the visual arts? Where does the Academy stand on conceptualism, on Rachel Whiteread and Damien Hirst? The Academy has its own postgraduate art school and its own education set-up, and does some good work with schools on how to teach the visual arts, but there is not enough sense of it publicly leading the debate. Its excellent current exhibition "Living Bridges" (proposals for inhabited bridges across the Thames) creates an agenda in architecture. Similar exercises in the fine arts are badly needed.
No doubt the current crisis will prompt the Royal Academy to take a careful look at its finances and perhaps its exhibitions programme. But it needs to do much more. It needs to work out what it stands for.