My first response was eaten by the internet.
Open your mouth wide and breathe out. Then purse your lips to whistle. It's not the air, it the interface between the air and the music that provides the music. Whether that interface is your voice box, your lips or an instrument of some kinds, it's not your breath alone that does it.
An interface is a unique, third aspect that allows two systems to interact.
What is the interface between my body and the air?
My voice box? No, that is part of my body
My lips? No, that is part of my body
An instrument would be an interface. It is a third element, but is it necessary? Can I create music without an instrument? Yes, I can. Singing, whistling, clapping, all of these can create music, and I do not need a third element to be between myself and the air to do them.
This is why I keep saying you are wrong about the interface being necessary for magic. It can be helpful. It can make sense to have one that increases the power, or amplifies it, or changes it into something else (how a flute can change the pitch of what you are doing in unique ways). But it is not logically necessary. There is no reason to say that a magic-user cannot interact directly with magic to create spells. There is no reason to say that a unique, third element is needed.
Just because we can use an interface, does not mean that it is absolutely necessary to have an interface. Many worlds and conceptions of magic do not require it, and in fact, see the uses of Interfaces as inferior methods of using magic.
Not true. It's supernatural, but not necessarily magic.
A distinction that is only useful if people make it useful. Since all magical phenomena are supernatural by definition.