I remain skeptical of statements that claim that one kind of model is categorically inferior. Also, I have a hard time believing this is a fair summary of the literature. First, one study is cited, but the sentence implies many.
Second, the citation in the original post is not a fair summary of the cited research. The abstract of "A Comparison of Event Models for Naive Bayes Text Classification" says: "This paper aims to clarify the confusion by describing the differences and details of these two models, and by empirically comparing their classification performance on five text corpora. We find that the multi-variate Bernoulli performs well with small vocabulary sizes, but that the multinomial performs usually performs even better at larger vocabulary sizes—providing on average a 27% reduction in error over the multi-variate Bernoulli model at any vocabulary size."