The origin of high-energy (HE) astrophysical neutrinos has remained an elusive hot topic in the field of HE astrophysics for the past decade. Apart from a handful of individual associations, the vast majority of HE neutrinos arise from unknown sources. While there are theoretically-motivated candidate populations, such as blazars -- a subclass of AGN with jets pointed towards our line-of-sight -- they have not yet been convincingly linked to HE neutrino production. Here, we perform a spatio-temporal association analysis between a sample of blazars (from CGRaBS catalog) in the radio and optical bands and the most up-to-date IceCube HE neutrino catalog. We find that if the IceCube error regions are enlarged by 1{deg} in quadrature, to account for unknown systematic errors at maximal level, a spatio-temporal correlation between the multiwavelength light curves of the CGRaBS blazars and the IceCube HE neutrinos is hinted at least at a 2.17{sigma} significance level. On the other hand, when the IceCube error regions are taken as their published values, we do not find any significant correlations. A discrepancy in the blazar-neutrino correlation strengths, when using such minimal and enlarged error region scenarios, was also obtained in a recent study by the IceCube collaboration. In our study, this difference arises because several flaring blazars -- coinciding with a neutrino arrival time -- happen to narrowly miss the published 90%-likelihood error region of the nearest neutrino event. For all of the associations driving our most significant correlations, the flaring blazar is much less than 1{deg} away from the published error regions. Therefore, our results indicate that the question of the blazar-neutrino connection is highly sensitive to the reconstruction of the neutrino error regions, whose reliability is expected to improve with the next generation of neutrino observatories.