We analyse 870 μm Atacama Large Millimetre Array (ALMA) dust continuum detections of 41 canonically selected z ≃ 3 Lyman-break galaxies (LBGs), as well as 209 ALMA-undetected LBGs, in follow-up of SCUBA-2 mapping of the UKIDSS Ultra Deep Survey (UDS) field. We find that our ALMA-bright LBGs lie significantly off the local IRX-beta relation and have relatively bluer rest-frame UV slopes (as parametrized by β), given their high values of the `infrared excess' (IRX ≡ LIR/LUV), relative to the average `local' IRX-β relation. We attribute this finding in part to the young ages of the underlying stellar populations but we find that the main reason behind the unusually blue UV slopes are the relatively shallow slopes of the corresponding dust attenuation curves. We show that, when stellar masses, M*, are being established via SED fitting, it is absolutely crucial to allow the attenuation curves to vary (rather than fixing it on Calzetti-like law), where we find that the inappropriate curves may underestimate the resulting stellar masses by a factor of ≃2-3× on average. In addition, we find these LBGs to have relatively high specific star-formation rates (sSFRs), dominated by the dust component, as quantified via the fraction of obscured star formation (f_obs≡ {SFR_IR/SFR_UV+IR}). We conclude that the ALMA-bright LBGs are, by selection, massive galaxies undergoing a burst of a star formation (large sSFRs, driven, for example, by secular or merger processes), with a likely geometrical disconnection of the dust and stars, responsible for producing shallow dust attenuation curves.