Scholars study representative international surveys to understand cross-cultural differences in mentality patterns, which are measured via complex multi-item constructs. Methodologists in this field insist with increasing vigor that detecting "non-invariance" in how a construct's items associate with each other in different national samples is an infallible sign of encultured in-equivalences in how respondents understand the items. Questioning this claim, we demonstrate that a main source of non-invariance is the arithmetic of closed-ended scales in the presence of sample mean disparity. Since arithmetic principles are culture-unspecific, the non-invariance that these principles enforce in statistical terms is "inconclusive" of encultured in-equivalences in semantic terms. Because of this inconclusiveness, our evidence reveals furthermore that non-invariance is "inconsequential" for the cross-cultural functioning of multi-item constructs as concerns their nomological linkages to other variables of interest. We discuss the implications of these insights for measurement validation in cross-cultural settings with large sample mean disparity.