Because of this, there seems to ba a qualitative difference between that, and a supernatural interaction, because if a supernatural thing isn't constrained by natural laws, then it can just as well be a one time event, unrepeatable, untestable, and unscientifically searchable.
The problem here is that you are assigning characteristics to the supernatural without even being able to show that the supernatural exists. Why can't the supernatural have predictable and testable interactions with the natural world? From what I have seen, the only reason that you are making this argument is that no one has found evidence for the supernatural. Therefore, the only way to defend the existence of the supernatural is to claim that evidence shouldn't exist if the supernatural is real. That doesn't sound like a good way to do things, at least to me.
In reading this thread I can't help but think of Harry Houdini. He spent a portion of his career debunking the psychics, mediums, and shucksters of his day. In fact, he greatly inspired Penn Jillette of Penn & Teller fame. This is why they demonstrate how magic tricks are done in the same way that Houdini demystified magic in his era. Each year Penn Jillette and a cadre of skeptics and Houdini family members get together for a seance. Before Houdini died he passed on three words to his wife so that she would know if it was really him speaking from the afterlife. These three words have been passed on through the family and are tightly held secrets. Every year the family invites people over to try to make contact with Houdini. So far, no luck even though mediums claim they have access to such information.
In the words of Penn Jillette, "Bullshit".
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