It came as Haines publicly castigated clients for demanding a top-class service from agencies for cut-price rates.
"I give clear warning that many agencies are operating too close to the wire for the good of our business or yours,
he told delegates.
"If you are disappointed in the lack of response from your agency to the new opportunities and threats proposed by the digital age, ask yourselves if you are expecting too much for too little."
But his attack on penny-pinching clients brought a swift and sharp response from Fisher, whose organisation commands an annual adspend of £195 million.
She claimed the problem was not clients' unwillingness to pay but the second-rate service many agencies provided.
"I find it hard to have any sympathy for agencies because I believe many of them have failed to evolve as fast as clients in terms of communications skills,
She cited the example of a recent pitch organised by COI for a large piece of business involving a number of top-20 agencies. "Not one presented a single decent integrated idea,
The meeting takes place against a background of increasing fears of senior agency figures that advertisers still perceive them as Ferrari-driving free-spenders when, often, agency pay now lags behind that of client companies.
Haines believes clients' reluctance to pay realistically is starving them of talent. He told delegates: "On the face of it, there should never have been a more exciting time to join our industry. That we are failing to attract our fair share of the available talent is worrying in the extreme."
Haines later said he hoped the meeting would help him to "better understand her frustrations about our business".
- Leader, p22.