Well, you're not exactly wrong but what you're saying is a bit weird. Technically something capable of arbitrary computation in the Turing machine sense can be

Well, you're not exactly wrong but what you're saying is a bit weird. Technically something capable of arbitrary computation in the Turing machine sense can be stronger than a Turing machine (the obvious example being a Turing machine with access to a halting oracle). Also if you want to show something is limited by the capabilities of a Turing machine it's way easier to point out it's being run on a Turing machine, as opposed to showing it's capable of arbitrary computation (which might not even be sufficient, as I explained above). As it stands it's not entirely obvious that a neural network with access to arbitrary precision arithmetic might not be more powerful than a Turing machine, but since we couldn't possibly construct a neural network precise enough that's a bit of a moot point.