[electromagnetic]

A person part of a militant group entering US territory with the express aim of subverting the US government would be invading, not rebelling.

If you're of the country and attacking it, you're a rebel. If you're not-of the country and attacking it, you're invading.

[stretchwithme]

That makes sense to me. I don't think you need to have an intent to control territory. Nor do I think we stop an examine things to make sure of the purpose.