Previous studies of the chemo-kinematic properties of stars in the Galactic bulge have revealed a puzzling trend. Along the bulge minor axis, and close to the Galactic plane, metal-rich stars display a higher line-of-sight velocity dispersion compared to metal-poor stars, while at higher latitudes metal-rich stars have lower velocity dispersions than metal-poor stars, similar to what is found in the Galactic disc. In this work, we re-examine this issue, by studying the dependence of line-of-sight velocity dispersions on metallicity and latitude in APOGEE Data Release 17, confirming the results of previous works. We then analyse an N-body simulation of a Milky Way-like galaxy, also taking into account observational biases introduced by the APOGEE selection function. We show that the inversion in the line-of-sight velocity dispersion-latitude relation observed in the Galactic bulge - where the velocity dispersion of metal-rich stars becomes greater than that of metal-poor stars as latitude decreases – can be reproduced by our model. We show that this inversion is a natural consequence of a scenario in which the bulge is a boxy or peanut-shaped structure, whose metal-rich and metal-poor stars mainly originate from the thin and thick disc of the Milky Way, respectively. Due to their cold kinematics, metal-rich, thin disc stars are efficiently trapped in the boxy, peanut-shaped bulge, and at low latitudes show a strong barred morphology, which – given the bar orientation with respect to the Sun-Galactic centre direction – results in high velocity dispersions that are larger than those attained by the metal-poor populations. Extremely metal-rich stars in the Galactic bulge, which have received renewed attention in the literature, do follow the same trends as those of the metal-rich populations. The line-of-sight velocity-latitude relation observed in the Galactic bulge for metal-poor and metal-rich stars are thus both an effect of the intrinsic nature of the Galactic bulge (i.e. mostly secular) and of the angle at which we observe it from the Sun.