Gregory Case, the consultant-turned-corporate-chieftain heading Aon Corp., is far too politic to suggest that the woes besetting so many financial behemoths may be a boon for Aon. But there’s a good chance that they will be.

Aon, after all, is no longer the loose conglomeration of insurance representatives that it was in April 2005, when Case left McKinsey & Co. to become chief executive of the Chicago-based company. He describes Aon as a tightly knit group of “colleagues” and “leaders” (he thinks words like “boss” and “employee” are needlessly divisive) who offer “risk management advice” (not “consulting,” the former consultant ...