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Calculations of the photoionization cross section of the $2p$ and $3s$ subshells of free Ar and Ar@${\mathrm{C}}_{60}$ as examples have been performed using the molecular structure of the confined system and time-dependent density functional theory for the dynamical quantities. The results for $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}2p$ in the combined system exhibit significant confinement resonances with the lower-energy ones being quite sharp, in contrast to the results of jellium-model calculations. In addition, calculations done with and without interchannel coupling between the photoionization channels of the $2p$ subshell of the Ar atom and the $1s$ subshell of the ${\mathrm{C}}_{60}$ shell show that, in this case, the coupling is of negligible importance, even though the $\mathrm{C}\phantom{\rule{0.28em}{0ex}}1s$ cross section is more than an order of magnitude larger than that of $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}2p$ in the 300 eV range. The $\mathrm{Ar}\phantom{\rule{0.28em}{0ex}}3s$, which is not hybridized, also exhibits confinement resonances, but is very strongly affected by interchannel coupling with photoionization channels from the ${\mathrm{C}}_{60}$ shell. The phenomenology of both $2p$ and $3s$ subshells is explained in terms of the interchannel-coupling matrix elements. These results should be applicable to inner-shell ionization of essentially any endohedral fullerene system.