Man arrested for 2x4 labeled "High Powered Rifle"
The fact that you disagree with the interpretation of the Second Amendment adopted by the United States Supreme Court in DC v. Heller does not make that interpretation a "deliberate misinterpretation."
http://en.wikipedia.org/wiki/District_of_Columbia_v._Heller
Many do participate in structured sports, including the incredibly-awesome sport of 3 Gun:
Team Benelli 3-Gun - YouTube
Other popular gun sports include skeet shooting, Olympic shooting, fullbore (a sport of British origin originally designed to give civilians marksmanship skills to supplement national defense), Bullseye (rimfire pistol marksmanship), Practical Shooting, etc.
The difference is, we don't think it's a good way to spend our very limited law enforcement resources to require a massive bureaucracy to prevent people from taking rifles they own home, or using them for hunting...especially not when massacres involving small-caliber handguns (Virginia Tech) or hunting rifles (Norway 2011) have been deadlier than any massacre ever involving "assault weapons" like the AR-15.
We don't fight DUIs by making more and more complex laws about what percentage of alcohol you can drink, requiring breathalizers be installed in every car, etc. We have simple laws and we enforce them. It's legal to drink. It's legal to drive. It's not legal to do both. You fight DUIs by getting cops on the streets looking for drunk drivers, not by banning the sale of whiskey on New Years' Eve. Likewise, I think America needs to stop gun crime by getting more cops out on the street, not by spending those dollars trying to regulate more which sorts of firearms are available.