Hurry to the Den and go to Mom's place. In the back you will find Karl, have him tell his story. Then tell him the people in Modoc believe him, and to go home. Return to Modoc and talk to Jo.
It's really easy to make this quest harder than it has to be. Whiskey Bob in Klamath, Stacey in the very same restaurant, and many other characters want you to buy them a drink. So does Karl, but in his case it doesn't make him want to help you, it makes him want to go to sleep. If you anger him, you may have to buy him a drink, but avoid it if you can; he will sleep for a couple of hours. If your doctor skill is high enough, you can revive him (and other drunks). If you listen to his story the first time you visit Den, you can save yourself a lot of legwork on the previous quest, but like Woody in the coffin, you'll have to come back to the Den to finish this one.