Early-time observations of Type II supernovae (SNe) 2013cu and 2013fs have revealed an interaction of ejecta with material near the star surface. Unlike Type IIn SN 2010jl, which interacts with a dense wind for ~1 yr, the interaction ebbs after 2–3 d, suggesting a dense and compact circumstellar envelope. Here, we use multi-group radiation hydrodynamics and non-local-thermodynamic-equilibrium radiative transfer to explore the properties of red-supergiant (RSG) star explosions embedded in a variety of dense envelopes. We consider the cases of an extended static atmosphere or a steady-state wind, adopting a range of mass loss rates. The shock breakout signal, luminosity and color evolution up to 10 d, and ejecta dynamics are strongly influenced by the properties of this nearby environment. This compromises the use of early-time observations to constrain R⋆. For dense circumstellar envelopes, the time-integrated luminosity over the first 10−15 d can be boosted by a factor of a few. The presence of narrow lines for 2–3 d in 2013fs and 2013cu require a cocoon of material of ~0.01 M⊙ out to 5−10 R⋆. Spectral lines evolve from electron scattering to Doppler broadened with a growing blueshift of their emission peaks. Recent studies propose a super-wind phase with a mass loss rate from 0.001 up to 1 M⊙ yr-1 in the last months or years of the life of a RSG, although there is no observational constraint that this external material is a steady-state outflow. Alternatively, observations may be explained by the explosion of a RSG star inside its complex atmosphere. Indeed, spatially resolved observations reveal that RSG stars have extended atmospheres, with the presence of downflows and upflows out to several R⋆, even in a standard RSG such as Betelgeuse. Mass loading in the region intermediate between star and wind can accommodate the 0.01 M⊙ needed to explain the observations of 2013fs. Signatures of interaction in early-time spectra of RSG star explosions may therefore be the norm, not the exception, and a puzzling super-wind phase prior to core collapse may be superfluous. Key words: radiation: dynamics / radiative transfer / supernovae: general