The key phrase is tell a lie not speak a falsehood. All the magic does here is reveal his honesty or dishonesty.

And since he eventually becomes either a real boy or ordinary puppet, it's hardly an infinite source of wood.

Excellent point that the only things worth invading Earth for are those things found only on Earth.

Seems kind of mean, cutting his nose off.

I suspect too many questions won't submit to a binary.

Pinnochio, Is light a wave?

There is a YouTube series about a lie detector like this.

Edit: here it is

It's only a lie if there is intent to decieve, he would have to know he's lying

This is a top-notch shower thought.

Ivory's rarer than wood though