Classic statistics done on compositional data is almost always wrong. In the past 20 years or so, a new statistical field called "compositional data analysis" has emerged to solve some of the problems arising from the closure problem. In short, it means that you have to transform all of your data to log-ratio form, do your stats, and transform it back. This can't solve all of the problems, however.
Now, the question is - do we care that it's wrong? In the vast majority of papers, there is hardly any statistics done of compositional data, and many correlations and trends are eyeballed and drawn by hand. Often, the hassle of doing statistics the correct way does not actually contribute everything. I've heard senior petrologists claim more than once that "if it looks like a line, it is a line. If it doesn't, then it is not a line. I don't need the R2 and p-values for that".