First of all, that equation is actually an equation for the change in x, not x itself. So even if it were uniformly valid, rather than being a classical simplification we teach to high school kids, it would still not tell you x unless you knew the original x at t=0. In other words, that answer is no answer at all-- it merely passes the buck for specifying the position to the initial condition. Secondly, if the initial x is well known, then it is your v that is not well known. So the equation tells us nothing at all in the context of the question you were asked-- which is why there is such a thing as quantum mechanics.

Moreover, these fundamental issues are not limited to our ability to know various things, say due to technological limitations, they have physical ramifications, like diffraction. The Bohmian picture that you favor does nothing to change that situation-- it allows one to imagine, with no predictive benefit whatsoever, that certain things are knowable but never actually known. To even entertain that notion is to have left objective science, obviously. Bohmian mechanics is not only pure philosophy, it's not particularly useful philosophy either. All it does is allow people to use classical pictures behind the quantum mechanics, while others use quantum mechanical pictures behind classical mechanics. In my opinion, either way that represents a simple loss of contact with what science actually is.