Can you conclusively prove that a higher power didn't influence evolution? No. That's because it's an article of faith for the people who believe it. Just because you don't agree doesn't mean you can trash their beliefs.
At the same time, its not even remotely science. Its an article of faith, and faith has no place in science.
You're falling into exactly the trap I've described of talking about ID without actually understanding what it is. For years creationist have been falling into its counterpart and coming up with spurious nonsense about the 2nd law of thermodynamics or how the lack of weird chimeras which are part mammal and part fish prove that evolution must be wrong.
I'm not rubbishing anyone's belief. I'm pointing out that the vast majority of people who claim to believe in ID actually believe in creationism because quite simply they do not understand what ID actually is.
If you want to talk about ID you must first understand what it is. ID attempts to be a scientific argument. It states that its three main concepts Irreducible complexity, Specified complexity and Fine-tuned universe prove that evolution must be wrong. It then further posits that there must be some sort of intelligent designer who dealt with these flaws by some mechanism.
And that is where ID stops. It doesn't say who the designer is. It doesn't say how the flaws were repaired it doesn't say anything beyond that. The designer could be aliens. The designer could be spagetti monster. It could be me travelling back in time and playing the ultimate practical joke on myself. ID stops at saying that there is a designer. ID goes out of its way to not say who or what the designer is.
The psuedo-scientific theory is then coupled to the faith based belief that God is the intelligent designer. Then and only then does faith enter into it. ID itself states nothing supernatural. It is only the gestalt entity that involves faith. ID itself is not an article of faith.
People who claim to believe in ID therefore are basically saying "I believe that there is scientific evidence that evolution is wrong. Therefore I believe in God". Can you not see how saying that ID is not scientific therefore automatically negates the entire first part of that argument. All you are left with is "I believe evolution is wrong. Therefore I believe in God".
If that's the case than so be it. You're entitled to that belief but why are you even mentioning ID at all? That phrase basically describes someone who is a creationist. Why bring ID into the matter at all?
If you are a proponent of ID you MUST believe its scientific. If you don't believe it's scientific you're just a creationist who hasn't caught on to the fact that ID is no longer relevant to you.