A phenomenological two-nucleon pion-absorption T matrix is used to calculate partial rates for absorption of negative pions from the 1s state of the $^{3}\mathrm{He}$ pionic atom. The T matrix depends on parameters ${g}_{0}$ and ${g}_{1}$, which describe absorption on s-wave triplet and singlet nucleon pairs, respectively. The partial rates considered are those feeding n+d, n${+}^{1}$(np${)}_{0}$, p${+}^{1}$(nn${)}_{0}$, and those nnp final states with no nucleon pairs of low relative energy. In addition, the differential rate to the nnp final state is calculated as a function of ${T}_{n}$ and ${T}_{p}$, observed neutron and proton kinetic energies, respectively, and is compared to experimental differential rates along selected straight lines in a Dalitz plot of event number density vs ${T}_{n}$ and ${T}_{p}$. Two different momentum space ground-state functions are used, both exhibiting the correct asymptotic behavior with respect to bound two-body and three-body channels but derived from wave functions in configuration space with and without hard-core nucleon-nucleon correlations. Agreement with a number of recent pion absorption experiments can only be obtained with the wave function containing hard-core correlations and only for small positive values of ${g}_{1}$/${g}_{0}$, ${g}_{1}^{2}$/${g}_{0}^{2}$0.04, much smaller than the ratio ${g}_{1}^{2}$/${g}_{0}^{2}$=0.30\ifmmode\pm\else\textpm\fi{}0.15, which is consistent with the low-energy production cross sections for p+p\ensuremath{\rightarrow}d+${\ensuremath{\pi}}^{+}$ and p+p\ensuremath{\rightarrow}p+p+${\ensuremath{\pi}}^{0}$. It is suggested that the discrepancy arises because gamma rays from pp bremsstrahlung may have contributed significantly to the measured ${\ensuremath{\pi}}^{0}$ production cross sections and/or because single nucleon processes may play a significant role in low-energy absorption on singlet nucleon pairs.