If you're talking about the case I think you are, that's not what was proved. What was proved was that an observer in a particular spot could be shown to be unable to detect whether a car stopped at a particular stop sign due to a combination of occlusion and the inability of the observer to detect actual velocity, substituting angular velocity instead.Interesting view. I think what you're saying is that math can't always perfectly model complex activities in the real world. I can see some basis for that claim although it can certainly perfectly reflect certain types of activities, such as, keeping track of how many apples one has on hand at any given time. When I say I have 10 apples and someone gives me 3 more and I use math to show that I know have 13 apples, that's not really an approximation. It's an exact value for the number of apples possessed.
On the other hand, if I want to model a non-linear process by assuming that it is linear, the result of the model will be approximations of the real-world process. It might be a good approximation or it might be a bad one, but that's not because the math is imprecise, it's because the model is based on an assumption and it is not actually performing the proper calculation--it is performing a different calculation (very precisely) to provide an approximation of the real-world process.
In this case, the approximation/estimate of lock time based on Newtonian physics will be imprecise because it is based on a number of assumptions. But the math itself is quite precise. If 100 people do the calculation the same, using the same inputs and assumptions, they will all get precisely the same answer.
Math, itself, is generally quite precise (since it was set up to be so, in general) although it can also be used to generate approximations, if desired.