I'm not sure what you're getting at. Classically we expect that given the same initial conditions, the outcome of a fluids experiment should always be the same. If an equation meant to describe fluid flows doesn't have this property, it is probably a bad model.

Not really. We know that the idea of a "fluid" has to break down eventually (at least due to finite particle sizes, possibly due to discretisations of space or whatever). An equation which describes "fluids" at sufficiently low resolution and breaks down once a resolution is reached where the idea of a "fluid" breaks down as well is then perfectly sufficient and, combined with the idea of a fluid, gives us as good model for reality.

Contrary to what the article claims here:

> the exact same fluid from the exact same starting conditions could end up in two distinct physical states, which makes no physical sense

it makes quite a lot of "physical sense" to get two possible outcomes out of one initial state, though we would not expect the Navier-Stokes equations to describe that situation.

The article is simply wrong in arguing that because we expect classical fluids to behave classically and because Navier-Stokes may break down in certain limits, NS may be a bad model. I actually struggle to put together a coherent sentence which comes close to what the article tries to say regarding the relation between "physical sense" and our expectations for the results of Navier-Stokes.