You're confusing the granting of a right with the defense of the right or enforcement of law.
Governments don't grant rights. We grant ourselves rights by the government we choose. You're confusing who's granting what. Government is an inanimate thing controlled by US. If it's not doing what you want, work to change it.
I get that, but you would feel you had a right to protect your own family, property, life, etc., even if there was no government there to help protect it for you. Hell even animals in the wild will protect their young, defend their den/nest, fight to protect their kill/food sources from scavengers, etc. IOW, even wild animals have a sense of rights. Thats why they're called "natural" rights. So what I mean is your hypothetical was irrelevant.
Sure you have a right to self defense. That's the only "natural right" I'd acknowledge, but it only goes as far as you're able to take it. To achieve the wider range of rights we enjoy requires a government to guarantee them, because very few would be able to do it on their own. If one can't assert it as a given in all circumstances, what makes it "natural"? It's actually unnatural, because it requires something NOT found in nature, an association we usually call "government".