Sure, I suppose someone could develop/copy something in parallel with no knowledge. But that's not really the case in the discussion here as it comes to former employees.
If you worked for Company A which uses a proprietary algorithm for trading and somehow created the same for Company B later, would you really expect a jury to think the two are unrelated? As stated above, the threshold is "more likely than not" that your work for Company B is related to knowing the trade secrets of Company A. If you had never worked for Company A, maybe, but again that's not the case here because a noncompete would never enter the picture.
I mean that’s a tad disingenuous as to how it worked before patents. Patents were meant to dissuade others from copying inventions for a certain set period. It was much rarer to see independent development of the same technology (not that it didn’t happen).
I guess I'm not seeing the point made. If you agree it wasn't developed in parallel, you copied it from your previous employer. If it was their IP, you likely committed a civil wrong, and they can sue you. I can only see your point if you don't believe IP exists.
A patent is an example that shows why that is a bad principle. The point of a patent is to share knowledge, but it also gives claims of ownership (for a period) to only a specific party. So obviously "knowledge of a product/process" isn't the discriminator. The important portion of a patent that distinguishes what is owned is literally called its "claims." My point is that whether or not you have knowledge does not lay claim to ownership, contrary to u/akira2501's question/point.