He makes a valid distinction, in a very specific sense. As long as we understand a program correctly, then we understand its behavior completely [0]. The same cannot be said of spherical cows (which, btw, can be modeled by computers, which means programs inherit the problems of the model, in some sense, and all programs model something).

However, that "as long as" is doing quite a bit of work. In practice, we rarely have a perfect grasp of a real world program. In practice, there is divergence between what we think a program does and what it actually does, gaps in our knowledge, and so on. Naturally, this problem also afflicts mathematical approximations of physical systems.

[0] And even this is not entirely true. Think of a concurrent program. Race conditions can produce all sorts of weird results that are unpredictable. Perfect knowledge of the program will not tell you what the result will be.