The WMAP Q-, V-, and W-band radial profiles of temperature deviation of the cosmic microwave background (CMB) were constructed for a sample of 31 randomly selected nearby clusters of galaxies in directions of Galactic latitude > 30^°. The profiles were compared in detail with the expected CMB Sunyaev-Zel'dovich effect (SZE) caused by these clusters, with the hot gas properties of each cluster inferred observationally by applying gas temperatures as measured by ASCA to isothermal β-models of the ROSAT X-ray surface brightness profiles, with the WMAP point-spread function fully taken into consideration. After co-adding the 31 cluster fields to significantly reduce the systematic and random uncertainties, it appears that WMAP detected the SZE in all three bands. Quantitatively, however, the observed SZE only accounts for about 1/4 of the expected decrement. The discrepancy represents too much unexplained extra flux: in the W band, the detected SZE corresponds on average to 5.6 times less X-ray gas mass within a 10' radius than the mass value given by the ROSAT β-model. We critically examined how the X-ray prediction of the SZE may depend on our uncertainties in the density and temperature of the hot intracluster plasma, and emission by cluster radio sources. Although our comparison between the detected and expected SZE levels is subject to a margin of error, the fact remains that the average observed SZE depth and profile are consistent with those of the primary CMB anisotropy, i.e., the overall WMAP temperature decrement among the 31 rich clusters is too shallow to necessitate an interpretation in terms of an additional effect like the SZE. A unique aspect of this SZE investigation is that because all the data being analyzed are in the public domain, our work is readily open to scrutiny by others.