It doesn't seem at all clear that Willingham was innocent. While his trial maybe shouldn't have happened because of flawed evidence, there has never been another explanation of what happened to leave his children dead under his care and allow him escape relatively unscathed.

In fact, while he, in hindsight, probably shouldn't have been executed for murder, he absolutely belongs in jail if for no other reason than the refrigerator positioning which doomed his children as much as anything else.

It is undisputed that Willingham's kids slept in the room where the fire broke out, while he slept in a different room. This is a pretty solid explanation for what happened.