  We obtained optical/near-IR rest-frame Magellan FIRE spectra (including
Pa$\beta$ and Pa$\gamma$) of 25 starburst galaxies at 0.5<z<0.9, with average
star formation rates (SFR) x7 above the Main Sequence (MS). We find that
Paschen-to-Balmer line ratios saturate around a constant value corresponding to
$A_{\rm V}\sim$2-3 mag, while line to IR luminosity ratios suggest a large
range of more extreme obscurations and appear to be uncorrelated to the former.
This behavior is not consistent with standard attenuation laws derived for
local and distant galaxies, while being remarkably consistent with observations
of starburst cores in which young stars and dust are homogeneously mixed. This
model implies $A_{\rm V}=$2-30 mag attenuation to the center of starburst
cores, with a median of ~9 mag (a factor of 4000). X-ray hardness ratios for 6
AGNs in our sample and column densities derived from observed dust masses and
radio sizes independently confirm this level of attenuation. In these
conditions observed optical/near-IR emission comes from surface regions, while
inner starburst cores are invisible. We thus attribute the high [NII]/H$\alpha$
ratios to widespread shocks from accretion, turbulence and dynamic disturbances
rather than to AGNs. The large range of optical depths demonstrates that
substantial diversity is present within the starburst population, possibly
connected to different merger phases or progenitor properties. The majority of
our targets are, in fact, morphologically classified as mergers. We argue that
the extreme obscuration provides in itself smoking gun evidence of their merger
origin, and a powerful tool for identifying mergers at even higher redshifts.
