In episode 2 “Infected” the only ones who had exhibited flu symptoms were Patrick, Karen, David, and the pigs/boar. Carol killed Karen and David and burned their bodies hoping that she could contain the sickness. But, her plan didn’t work as we saw in last night’s episode when others started showing symptoms, too.
I think Carol doesn’t want a repeat of what happened to Sophia, so that’s why she’s been teaching the kids how to use knives, etc.
...that we saw. Don't forget, what we see in the foreground doesn't mean something isn't goin on in the background..........
Now, you can believe that Carol killed/murdered Karen and David prior to their turning and your only evidence is Hershel making the claim, but I prefer not to.