  (Abridged) Many of the observed CO line profiles exhibit broad linewidths
that greatly exceed the thermal broadening expected within molecular clouds.
These suprathermal CO linewidths are assumed to be originated from the presence
of unresolved supersonic motions inside clouds. Typically overlooked in the
literature, in this paper we aim to quantify the impact of the opacity
broadening effects on the current interpretation of the CO suprathermal line
profiles. Without any additional contributions to the gas velocity field, a
large fraction of the apparently supersonic (${\cal M}\sim$2-3) linewidths
measured in both $^{12}$CO and $^{13}$CO (J=1-0) lines can be explained by the
saturation of their corresponding sonic-like, optically-thin C$^{18}$O
counterparts assuming standard isotopic fractionation. Combined with the
presence of multiple components detected in our C$^{18}$O spectra, these
opacity effects seem to be also responsible of the highly supersonic linewidths
(${\cal M}>$8-10) detected in the broadest $^{12}$CO and $^{13}$CO spectra in
Taurus. Our results demonstrate that most of the suprathermal $^{12}$CO and
$^{13}$CO linewidths could be primarily created by a combination of opacity
broadening effects and multiple gas velocity components blended in these
saturated emission lines. Once corrected by their corresponding optical depth,
each of these gas components present transonic intrinsic linewidths
consistently traced by the three CO isotopologues within a factor of 2. Highly
correlated and velocity-coherent at large scales, the largest and highly
supersonic velocity differences inside clouds are generated by the relative
motions between individual gas components. This highly discretized structure of
the molecular gas traced in CO suggest that the gas dynamics inside molecular
clouds could be better described by the properties of a fully-resolved
macroscopic turbulence.

Astrophysics of Galaxies