The first year of JWST has revealed a surprisingly large number of luminous galaxy candidates beyond z>10. While some galaxies are already spectroscopically confirmed, there is mounting evidence that a subsample of the candidates with particularly red inferred UV colors are in fact lower redshift contaminants.These interlopers are often found to be HST-dark or optically-fain galaxies at z~2-6, a population key to understanding dust-obscured star formation throughout cosmic time. This paper demonstrates the complementarity of ground-based mm-interferometry and JWST infrared imaging to unveil the true nature of red 1.5-2.0 um dropouts that have been selected as ultra-high-redshift galaxy candidates. We present NOEMA Polyfix follow-up observations of four JWST red 1.5-2.0 um dropouts selected by Yan et al. 2023 as ultra-high-redshift candidates in the PEARLS field. The new NOEMA observations constrain the rest-frame far-infrared continuum emission and efficiently discriminate between intermediate- and high-redshift solutions. We report >10sigma NOEMA continuum detections of all our target galaxies at observed frequencies of 236 and 252 GHz, with FIR slopes indicating a redshift z<5. We model their optical-to-FIR spectral energy distribution (SED) with multiple SED codes, and find that they are not z>10 galaxies but instead dust-obscured, massive star-forming galaxies at z~2-4. The contribution to the cosmic star-formation rate density of such sources is not negligible at z~3.5 (phi > 1.9-4.4 x10^-3 cMpc^-3), in line with previous studies of optically-faint/sub-millimeter galaxies. This work showcases a new way to select intermediate- to high-redshift dust-obscured galaxies in JWST fields with minimal wavelength coverage to open a new window on obscured star-formation at intermediate redshifts