So, I really can't think of anymore to tell you than this. If my argument does not persuade you, I can't do a whole lot.
If Hidan were to slice an artery open, what happens? The same injury appears on the other person. So, seeing as the Chakra system runs through the body in the exact same way that veins do, you can injure the chakra system PHYSICALLY. There is no other way to do it. The Gentle Fist literally proves that you can PHYSICALLY hit the Chakra Network, so long as you know where it is. Anyone can know where all 360+ Chakra Points are, but that doesn't mean they can strike them during battle without the Byakugan.
As for the fire state, look at it like this; You turn to fire, okay. This stops things like knives, fists, physical attacks from hurting you. BUT! Damage to the chakra system still ensues. A Hyuuga can hit you in your fire state without hurting themselves so long as they are using the Gentle Fist. How? Because that is what they do. Hyuuga destroy chakra, chakra points, anything like that. It's their job. That alone proves that, even in a fire state, you can still physically take damage. Now, you can't shed blood. If Eikan were to have tried to rip a limb off or dismember your body, then it wouldn't work... But you are talking about INTERNAL damage, but not just any normal internal damage. You get rid of your bones, skin, muscle, even your eyes and what do you have left? You chakra network. You CANNOT change how that works, not without basically destroying your whole network and rewriting it instantly, which is also impossible and not written down anywhere.
By simply stating you are in fire form, you are screwing yourself over. How? Because what lets you turn into fire? That's right, chakra does. Maybe if you weren't using chakra and someone, not Kurama, was funneling chakra to you through some long distance, then maybe you could argue that it isn't working. But you can't, because your chakra network is constantly active to turn you into fire. It IS there, and seeing as you did NOT turn you chakra system into fire(Because then it couldn't generate, you know, chakra), the damage is still the same.
It may not be the normal physical damage that one is use to talking about, but the chakra system IS there and CANNOT be changed, therefore damage done to it still would carry over.