We consider pressure-driven flows of electrolyte solutions in small channels or capillaries in which tracer particles are used to probe velocity profiles. Under the assumption that the double layer is thin compared to the channel dimensions, we show that the flow-induced streaming electric field can create an apparent slip velocity for the motion of the particles, even if the flow velocity still satisfies the no-slip boundary condition. In this case, tracking of the particles would lead to the wrong conclusion that the no-slip boundary condition is violated. We evaluate the apparent slip length, compare it with experiments, and discuss the implications of these results.