Most of the applications today, especially in streaming data, generate hundreds of variables coming from different sensors at the same time. Is it wise to call such data 'Multivariate' even when several or, maybe all, of these variables are independent and do not correlate with one another? Wouldn't simply considering any dataset with multiple variables as multivariate and applying usual data-science procedures (standardization, clustering, etc.) distort the inherent properties or lead to unreliable estimates?

In short, what are the properties that a multivariate (Gaussian or non-gaussian) data must follow?