Background: The ($p,p\ensuremath{\alpha}$) knockout reaction is useful for the study of preformed $\ensuremath{\alpha}$ clusters in atomic nuclei. At quasifree kinematic conditions above an incident energy of about 100 MeV the cross section and analyzing-power angular distributions extracted from the ($p,p\ensuremath{\alpha}$) knockout reaction are anticipated to resemble its free two-body counterparts. Several ($p,p\ensuremath{\alpha}$) knockout studies in the incident-energy range of 100--150 MeV on targets up to $^{12}\mathrm{C}$ confirm the predicted equivalence. However, the only experiment on $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ appears to fail the expectation spectacularly.Purpose: The reason for the drastic discrepancy between the experimental analyzing-power angular distribution for $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ and the trend of free elastic scattering of protons from $^{4}\mathrm{He}$ is investigated.Method: Guidance in general from the distorted-wave impulse approximation (DWIA) theory is employed. Specific focused theoretical calculations are performed.Results: As expected, for the ($p,p\ensuremath{\alpha}$) reaction on several light target masses up to $^{12}\mathrm{C}$, comparable cross section and analyzing-power angular distributions resemble free $^{4}\mathrm{He}(p,p)^{4}\mathrm{He}$ elastic scattering to a remarkable extent. The DWIA treatment for the $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ reaction, however, needs a more careful selection of the distortion optical-model parameters in the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ar}$ outgoing channel. Global optical-model potentials used in the published work reproduce neither analyzing-power distribution of the $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ reaction, nor $\ensuremath{\alpha}\text{\ensuremath{-}}^{36}\mathrm{Ar}$ elastic scattering cross-section angular distributions. Use of appropriate optical potentials resolves the problem.Conclusions: The use of appropriate optical-model potentials which describe elastic scattering of $\ensuremath{\alpha}$ particles from $^{36}\mathrm{Ar}$ correctly appears to be crucial. The problem reported previously in the literature is resolved to a remarkable extent. There is a need to explore the two-body aspects of the quasifree ($p,p\ensuremath{\alpha}$) reaction for heavier targets further.