Physical fighting is violence that often leads to death.
And I quoted from the Sahih Bukhari 6924 when Muhammad said, "I have been ordered to fight the people till they say: 'None has the right to be worshipped but Allah, 'and whoever said, 'None has the right to be worshipped but Allah', Allah will save his property and his life from me"
As long as they worship God as Muhammad commanded they could keep their property and their lives.
Meaning - if they someone did not agree with Muhammad - he would either kill them or take their stuff or both.
Is that a Hadith? I believe(and I could be wrong)that the Hadith are open to interpretation.
There is more to the idea of to 'fight' than just broad killing. It can certainly lead to death, but doesn't always. And in some cases, fighting is through a totally different action. If I say "I'm fighting my parking ticket in the courts", it doesn't mean I'm going to walk into court and attempt to beat up the judge.