Basic idea: acting in a socially responsible is more valuable to those firms with bad reputations. Therefore, following a disaster, these are the firms that are more likely to give (since they have the most to gain).
From the paper:
"We find Hurricane Katrina had a significant negative impact on firms’ stock prices. Further, we find that the more a firm was known for bad deeds, the greater the drop in its market value during Katrina, and the greater the likelihood of engaging in corporate philanthropic disaster response (hereafter ―CPDR‖) after Katrina."