I'd say theoretical proofs of impossibility tend to make valid logical deductions within the formal model they set up, but the issue is that model often turns out to be a deficient representation of reality.
For instance, Minsky and Papert's Perceptrons book, credited in part with prompting the 1980s AI winter, gives a valid mathematical proof about inability of networks within their framework to represent the XOR function. This function is easily solved by multilayer neural networks, but Minsky/Papert considered those to be a "sterile" extension and believed neural networks trained by gradient descent would fail to scale up.
Or more contemporary, Gary Marcus has been outspoken since 2012 that deep learning is hitting a wall - giving the example that a dense network trained on just `1000 -> 1000`, `0100 -> 0100`, `0010 -> 0010` can't then reliably predict `0001 -> 0001` because the fourth output neuron was never activated in training. Similarly, this function is easily solved by transformers representing input/output as a sequence of tokens thus not needing to light up an untrained neuron to give the answer (nor do humans when writing/speaking the answer).
If I claimed that it was topologically impossible to drink a Capri-Sun, then someone comes along and punctures it with a straw (an unaccounted for advancement from the blindspot of my model), I could maybe cling on and argue that my challenge remains technically true and unsolved because that violates one of the constraints I set out - but at the very least the relevance of my proof to reality has diminished and it may no longer support the viewpoints/conclusions I intended it to ("don't buy Capri-Sun"). Not to say that theoretical results can't still be interesting in their own right - like the halting problem, which does not apply to real computers.
This is really, really common. And it's done both by mistake and in bad faith. In fact, it's a guarantee that once anybody tries anything different enough, they'll be constantly attacked this way.