This doesn’t sound right, if they don’t know the structure of the NN how can the reconstruct from the weights alone? (Perhaps the structure is communicated within the weights?)
Every agent training the model on their proprietary data has to have access to the model form in some way (otherwise how would they train it?)
For this reason, one must assume that the model form is known to the adversary.
With this, the question becomes: is it possible to reconstruct training data from a trained model? We already know that, at least for some image models, the answer to that question is "yes": https://arxiv.org/pdf/2301.13188.pdf
I don't think lossy compression is sufficient. The very first example in the paper I linked to is clearly not identical to the original image (=lossily compressed) yet leaks a training image in a way that would be highly problematic in certain domains, e.g. medical imaging.
I see what you are saying. Agree. Seems we need some set patterns in NN models that will reliably remove reversibility without effecting loss too drastically.