Activist investors like Bill Ackman, Carl Icahn and Nelson Peltz have been striking terror in corporate boardrooms for some time. But CEOs and directors have a new reason to grab for the Zantac, it seems: some very big shareholders are starting to listen to them. Once-quiet and conflict-averse asset managers are giving the arguments made by activist attackers more deliberative consideration these days—and they’re putting pressure on corporate managements to respond to those criticisms in substantive ways, an all-star panel told the invite-only crowd at Fortune’s Global Forum Tuesday afternoon.

“When there is an activist situation, we do meet with him,” said Michelle Edkins, a managing director and global head of corporate governance and responsible investment at powerhouse BlackRock (“BLK”). “We want to hear what it is the activist thinks the company can do better. What change is going to make this company stronger for the long term?”

Fundamentally, that comes down to two areas, noted Peter Michelsen, a one-time Goldman Sachs managing director who is now a partner at CamberView, a San Francisco firm that counsels public companies on shareholder activism and engagement. There’s the straightforward argument “on the economic side—the ability to make money,” said Michelsen—whether that’s strategic (Should the company spin, sell, or shut operations?) or operational (Are there efficiencies that could be exploited that the current management is missing?).

But the more critical issue, said both Michelsen and Edkins, is trust. Big institutional investors are increasingly spending the time and effort to determine if a company’s management team and board have been “credible” with their past promises and that they have an equally credible strategy to drive the company forward.

“Ultimately, it comes down to trust,” said Michelsen. “Investors want to make sure the board is not captured by management” and that the CEO and other top executives “truly have the courage of their convictions, whether it’s driving the business harder or a strategic overall.”

Michelsen and Edkins, likewise, agreed that CEOs and boards who try to strong-arm or flatly dismiss the criticisms of activists often do so at their own peril. “It’s important to figure out where the activist may have a point,” said Michelsen. “Engaging with them and understanding what their thesis is,” he said, “is always the right answer in my book.”

Indeed, said Edkins, the activist assaults over the past several years have already helped companies and their shareholders in a profound way by “shifting conversations in the boardroom.” More and more boards of directors are asking themselves: “How do we make sure we’re being our own activist? How do we make sure we understand what’s driving the business and what our vulnerabilities are?”

Sometimes, as it happens, those discussions lead to finding better partners (or suitors) for a company than the one launching the outside attack.

That was the case with Allergan, said panelist David E. I. Pyott, the one-time chairman and CEO of the botox-maker, who found himself out of a job earlier this year when the company was acquired by Actavis (“ACT”)—now called Allergan again—and who engaged in his own epic and bitter battle with Valeant Pharmaceuticals (“VRX”) and Pershing Square’s tenacious Bill Ackman.

And Pyott has a convincing piece of evidence to back up his assertion: the market. At the close of the deal, the company Pyott ran was valued at $71 billion, he told the room. That was some $25 billion more than what Valeant had offered at the outset in April 2014.

Seems like shareholders ended up with the better deal.