No, I think one of the fundamental insights of stochastic calculus is that the addition of noise to a process changes the trajectory in a non-trivial way.

In finance, for instance, it leads to the concept of a "volatility tax." Naively, you might think that adding noise to the process shouldn't change the expected return, it would just add some noise to the overall return. But in fact adding volatility to the process has the effect of reducing the expected return compared to what you would have in the absence of volatility. (This is one of the applications of the result that the original article talks about in the Geometric Brownian Motion section.)