Cowbirds are brood parasites, which means that they lay their eggs in the nests of other birds for those other birds to raise. Some birds actually recognize cowbird eggs and throw them out of their nests, but many don't. From what I've seen, cowbird eggs look very similar to cardinal eggs. I couldn't tell the difference, at least. I doubt that Edna would have been able to.
Another interesting fact, though, is that cowbirds do check up on the nests of the birds they laid their eggs in to see how their kids are doing. This is to see if they did well in that nest so they know if they should lay eggs in that same nest next time.