Mark Joseph Stern at Slate has, by far, the best quote to sum up everything that is wrong with legally allowing adults to hit children in the United States:
[Adrian] Peterson's case reveals a broader problem with America's child-abuse laws: It's surprisingly difficult to tell where legal corporal punishment ends and criminal child abuse begins—and so long as the former is allowed, the latter seems bound to occur. [Emphasis mine]
The most ironic theme of this national debate is that the pro-corporal punishment crowd looks at Peterson and says, "Oh that isn't what we meant," while the foundation of Peterson's defense lies in his firm alliance with that very same bunch. (Reggie Bush aligns himself with this group as well.) Note in his written response, Peterson walks it back a little bit but never explicitly says that hitting a child is wrong. (I'm sure that was the best his legal team could get him to agree to.)
The problem is that for every person who is okay with an over-the-clothes-once-in-a-lifetime spanking but is horrified by the Peterson case, you get someone else who doesn't bat at eye. Nothing ever gets done to address this problem, and the world goes on until another high-profile parent gets caught.
The only way to substantively address this problem is to prohibit corporal punishment altogether. Permitting grey areas isn't feasible, and there's no way it can be. As long as there is latitude, someone will take it too far either in anger or in horrific views of "discipline" or both.
Perhaps that's why Scandinavian countries already outlawed corporal punishment decades ago. They really are a group of people who can honestly say, "I turned out just fine!" and mean it.