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A recent cross-correlation of the ROSAT all-sky survey (RASS) with the IRAS point source catalog purported to reveal a large number of luminous ($L_{\rm x} \sim 10^{42} - 10^{44} \ {\rm ergs\ s}^{-1}$) X-ray galaxies with optical classifications as normal spirals and starbursts, not\/ AGNs (Boller et al. 1992, A\&A, 261 , 57). This result led to claims of a class of X-ray-bright spiral galaxies. Our optical spectroscopy of a number of these high $L_{\rm x}$ objects, as well as careful examination of the literature, confirms that while several are misclassified AGNs, others show no indications of nuclear activity at all. The existence of any high $L_{\rm x}$ ``normal'' galaxies would be of considerable interest, not only because of the extreme nature of the violent processes occuring within them, but also because of the impact a population of such objects could have on the problem of the unexplained cosmic X-ray background. However, a detailed statistical analysis of the ROSAT/IRAS sample clearly demonstrates that objects with large X-ray/IR (or X-ray/optical) position offsets have a very high probability of being chance X-ray/IR coincidences, and, furthermore, that the putative high-$L_{\rm x}$ galaxies are overrepresented amongst the group with the largest offsets. In one case, the X-ray position falls directly on a bright star $81^{\prime\prime}$ away from the starburst galaxy, assuring that this match is indeed a chance coincidence. We have\/ found that at least two of the high $L_{\rm x}$ starbursts are correctly identified with an RASS X-ray source, although the case for a population of these objects is much less certain. Our analysis has, of course, been hampered by the fact that we have no access to the RASS. Nonetheless, our results lead us to view as unproven the claim that there exist starburst galaxies without active nuclei that have soft X-ray luminosities substantially in excess of $10^{42} \ {\rm ergs\ s}^{-1}$.
\smallskip This work was supported by NASA under grant NAGW-2507.
