SVMs were invented by a couple statisticians/mathematicians in the 60s. k-means also harkens back to the 60s, by mathematicians and control theorists. Decision Trees and Random forests were invented by a famous statistician, with the latter related to bootstrapping, a statstical technique. PCA and factor analysis, forms of or closely related to low rank matrix approximation, were pioneered in the early 1900s, by some of the most famous statisticians ever.
Something that was invented by a statistician is not necessarily statistics, and that certainly applies even more to something invented by a mathematician. I guess with a broad enough notion of statistics some of these would fall in the field of statistics, but if something does not use at least one probability distribution it's probably far fetched to classify it as statistics.
It would be a lot more fair to classify machine learning as a subfield of convex optimization. Yet even that classification does not quite fit, so it makes most sense to just accept that it's a separate field which uses techniques from statistics, convex optimization, computer science, and more.
