Certainly. Simply because one cannot both know position and velocity through measurement, for example, doesn't prevent the idea that if one did know both, then they could present with certainty the outcome. One might suggest a metaphor: if you were trying to aim a cannon and you measured exactly one of the angle of inclination or the amount of powder in the cannon, you would be presented with a range of possibilities and it might seem random. But if you did know both the angle and the powder, then you could predict the behavior of the shot with great accuracy. In the context of quantum mechanics, these theoretical additional pieces of information are called hidden variables.
Of course, this is a flawed metaphor. It happens to be more common for physicists to not believe this, or rather that it does not make sense to talk about both the position and the velocity of a particle with certainty, and instead you must think of them stochastically. Focusing on smaller subsystems causes certain parts to suddenly be more in focus and others collapse entirely. This is referred to as wave function collapse, and it seems to be at the core of both indeterminism in measurement and the indeterminism of a system. If we followed the heart of the argument, it might actually be the case that inability to measure things precisely is exactly what leads to quantum indeterminism, but I must admit that I do not know this.
There is some confusion on this, and this talked about at physics.se several different times (clicking on the related links on those is a good avenue for further exploration). There are even different interpretations of the same sets of facts.
Perhaps most important here is Bell's Theorem, which says roughly that a theory incorporating local hidden variables will never agree fully with quantum mechanics (note the local bit here). So following our local model of quantum mechanics, it truly does not make sense to talk about knowing both the position and the velocity (for example) of a particle, and thus wave function collapse is inevitable. And this brings us back to the Measurement problem.
So in short, the fact that we can't measure all quantities arbitrarily well leads to indeterminism, which leaves room for free will.
On the other hand, if we were capable of measuring all quantities arbitrarily well, and if the resulting model were completely deterministic (which it might be, as then there would be no need for wave function collapse), then it might not make sense to talk about free will. And thus much of what your physicist friends have said have a kernel of truth to them.