In a perfect world, that would, perhaps, be true. Because in a perfect world, everyone would, perhaps, exercise their rights responsibily. The reason that government has a "right" (some would say "duty" or "obligation" rather than "right") to infringe on people's "rights" is that people do not always exercise their rights responsibily. In this imperfect world of ours, the idea that rights imply a certain amount of responsibility in their exercise has been forgotten or ignored. Everyone is up in arms about their "rights", but no one seems to be talking about the responsibilities that go along with the exercise of any given right. Nancy Lanza was well within her 2nd Amendment rights to possess the guns her son, Adam, used to kill those 20 children and 7 adults in Newtown, but there is also no doubt that those guns were used irresponsibily. I believe in the 2nd Amendment as much as anyone else does, but I also believe in the responsible exercise of 2A rights. Unfortunately, not everyone with access to a gun believes the same, and this is why the government is involved in the whole mess.
The only responsibility that goes along with rights is the negative responsibility to leave others alone to exercise theirs freely. True rights are never in conflict. Your rights end where the equal rights of others begin. Either you are acting within your rights, or you are violating someone else's. Obviously we don't live in a "perfect world," and people do sometimes violate the rights of others. When this happens, the violator should have force brought against him, in defense of the victims' rights. But it is unjust to violate ANYONE'S rights who is not threatening those of anyone else... and it is HORRIBLY unjust to preemptively violate everyone's rights to try to reduce the harm of a few bad actors.