Large star-to-star variations of the abundances of proton-capture elements, such as Na and O, in globular clusters (GCs) are interpreted as the effect of internal pollution resulting from the presence of multiple stellar populations. To better constrain this scenario, we investigate the abundance distribution of the heavy element rubidium (Rb) in NGC 6752, NGC 1904, and NGC 104 (47 Tuc). Combining the results from our sample with those in the literature, we found that Rb exhibits no star-to-star variations, regardless of cluster metallicity, with the possible intriguing, although very uncertain, exception of the metal-rich bulge cluster NGC 6388. If no star-to-star variations can be confirmed for all GCs, this finding implies that the stellar source of the proton-capture element variations must not have produced significant amounts of Rb. This element is observed to be enhanced at extremely high levels in intermediate-mass asymptotic giant branch (IM-AGB) stars in the Magellanic Clouds (i.e., at a metallicity similar to 47 Tuc and NGC 6388). This fact may present a challenge to this popular candidate polluter, unless the mass range of the observed IM-AGB stars does not participate in the formation of the second-generation stars in GCs. A number of possible solutions are available to resolve this conundrum, including the fact that the Magellanic Cloud observations are very uncertain and may need to be revised. The fast rotating massive stars scenario would not face this potential problem as the slow mechanical winds of these stars during their main-sequence phase do not carry any Rb enhancements; however, these candidates face even bigger issues such as the production of Li and the close overlap with core-collapse supernova timescales. Observations of Sr, Rb, and Zr in metal-rich clusters such as NGC 6388 and NGC 6441 are sorely needed to clarify the situation.