I think there is some confusion here. This page is discussing Bayesian multivariate linear regression, but there is no page on multivariate linear regression from a non-Bayesian perspective. I think people are getting confused between multiple regression and multivariate regression. The former has a scalar as the response whereas the latter has a vector as a response. There is a link to 'multivariate linear regression' but it (wrongly) takes you to 'The General Linear Model' which would be appropriate for multiple regression.