N-S aren't "right" though. The derivations make a lot of good assumptions that breaks down in certain materials/situations.
What is right is its starting point on the conservation of momentum and energy. Then it makes certain assumptions about the stress-tensor which are not necessarily true. Meaning, you can derive the N-S from consv. of mass and E and a certain stress tensor (ST), but its not derived from a universal ST.
NS are a pretty good model for the underwater scenarios a Navy would be interested in, so I think they can be called "right" here. The fluids are regarded as "Newtonian" so the stress tensor model is good, and the density of the fluid is high enough that the continuum approximation is good. The largest source of error is likely the approximations made to model the turbulence, or in other words, reduce the computational complexity while also reducing accuracy.
What is right is its starting point on the conservation of momentum and energy. Then it makes certain assumptions about the stress-tensor which are not necessarily true. Meaning, you can derive the N-S from consv. of mass and E and a certain stress tensor (ST), but its not derived from a universal ST.