The identification of high-redshift, massive galaxies with old stellar populations may pose challenges to some models of galaxy formation. However, to securely classify a galaxy as quiescent, it is necessary to exclude significant ongoing star formation, something that can be challenging to achieve at high redshifts. In this letter, we analyse deep ALMA / 870 µm and SCUBA-2 / 450 µm imaging of the claimed "post-starburst" galaxy ZF-20115 at z = 3.717 that exhibits a strong Balmer break and absorption lines. The far-infrared imaging reveals a luminous starburst located 0.4 ± 0.1 (∼ 3 kpc in projection) from the position of the rest-frame ultra-violet / optical emission, with an obscured star-formation rate of 100 +15 −70 M yr −1 . This star-forming component is undetected in the restframe ultraviolet but contributes significantly to the lower angular resolution photometry at restframe wavelengths > ∼ 3500 Å, significantly complicating the determination of a reliable stellar mass. Importantly, in the presence of dust obscuration, strong Balmer features are not a unique signature of a post-starburst galaxy and are indeed frequently observed in infrared-luminous galaxies. We conclude that the ZF 20015 system does not pose a challenge to current models of galaxy formation and that deep sub-/millimeter observations are a pre-requisite for any claims of quiescence. The multiwavelength observations of ZF 20115 unveil a complex system with an intricate and spatially-varying star-formation history. ZF 20115 demonstrates that understanding high-redshift obscured starbursts will only be possible with multi-wavelength studies that include high-resolution observations, available with the JWST, at mid-infrared wavelengths.