Many early images of the Buddha look like this one - came into being after Alexander the Great invaded Bactria. It's the Buddha, not Apollo.
It's images like this that come to my mind when I hear people make generalizations about Buddhists, and Western Buddhists in particular, as to whether they are authentic or not. It's the flip side to the other problem - the relative invisibility of Asian Buddhist communities to Western Buddhist communities. And so occasionally I have heard remarks from some people who do not take Western Buddhists seriously (and they are not all of European descent). But as the above picture shows, it is likely there were Western Buddhist practitioners before there were Korean or Japanese practitioners. And yes, indeed, it is because of Western imperialism...usurping Persian and Indian imperialism all of which had long been rendered irrelevant by the time the Mongols arrived.
And the history's not so important as the practice.