Imperfect information plays a role in our economy. For example, a person diagnosed with a fatal illness may like to purchase life insurance for his family even if he had to pay an actuarially fair (thereby, high) price. But life insurance companies will not sell insurance to such a person because the cost of verifying exactly how fatal is his illness (expensive doctors and testing would have to be hired) exceeds the patient's willingness to be insured.
Imperfect information cannot stop a transaction with billions of dollars of benefits unless the costs of verifying that information is even greater than that.
Professor Kashyap and Diamond are blaming lack of troubled bank equity sales on imperfect information. Specifically, they say that a fairly strong bank would fail to raise equity because investors fear that the bank is actually quite weak (i.e., have some hidden troubled assets). They error both in fact and in logic. In fact, troubled banks have raised some equity from the private sector, which demonstrates that information problems have been overcome in this situation.
Regarding the logic, their story has some sense to it if it were a story about a small bank. But they are applying that story to the large banks (such as those receiving the "equity injections" from the U.S. Treasury) who have hundreds of billions of dollars in assets. Whatever private information those bank managers have could be made sufficiently public (or revealed to a single large scale investor) or sufficiently incentivized for far less than billions of dollars.
I suppose that the Professors would say that "it takes too long to make those discoveries." Where is the evidence for that claim? How many hours did the bank managers currently (and allegedly) holding the private information take to acquire it in the first place? Haven't some of these banks known for months that they would need more equity -- why weren't those months long enough to sufficiently publicize the private information? Why can't some of the managers in-the-know be made part of a new investment group and thereby given an incentive to blow the whistle? A lot of problems can be sufficiently solved in short order when there are billions at stake.
A more coherent story for the lack of equity sales is that the cost of capital is too high (many investors do not want to own bank stock regardless of what a detailed audit would show) and, even if it weren't, subsidized public capital is on the horizon and raising private equity would make them less eligible for the subsidy.