As I understand it, in America "it's just a tool" is shorthand for "guns should be regulated like hammers, i.e. barely at all, responsibility lies with the user not those who make, market and sell it"

You're partially right about the responsibility part, but I think the rest is going too far. The phrase is a direct response to media and gun control advocates who treat the existence of guns as the cause of crime instead of the people using the gun.