Proton-proton collisions at RHIC are generally considered a "clean apples-to-apples reference" crucial to the study of high-pT physics in heavy ion collisions at RHIC. Is there anything to be learned through similar comparisons in the soft sector? Usually, the trends in soft physics observables in central A+A collisions are understood as arising from collective hydro-like radial flow from a bulk system. On the other hand, little flow is expected to arise in the low-pT sector of proton-proton collisions (the "underlying event"), due to the low particle multiplicity. In this talk, I will challenge this assumption. I will discuss the effects of phasespace constraints due to conservation laws, directly measured in two-particle correlations, and how these constraints distort single-particle spectra. If phasespace constraints are taken into account, a consistent picture emerges from spectra and HBT correlations, pointing to very similar explosive flow in proton and heavy ion collisions.