Yes, tao is found in the context of buddhist thought. But is it an original buddhist concept or has it just been integrated into buddhist thought? This to me makes a difference. And has it or how has it been modified by being incorporated?
My 2-cents' worth, as I am not an expert on this topic, by any means... From what I've read in various historical writings, the concept of Tao and Taoism as a philosophy were already well established in China by the time Buddhist monks brought Buddhism there from India. Because Taoism was not a religion, and a number of its concepts were compatible with many aspects of Buddhist thought, the two easily meshed and resulted in Buddhist sects with varying degrees of Taoist thought integrated into them. Probably, Buddhism already had a number of like- or very similar concepts when it met Taoism, which is why the two were able to "hit it off."
That said, there were a lot of misunderstandings between the two systems due to the Babel of languages and dialects into which tracts of Taoism and Buddhism were translated and taught. So, a lot of the same words and terminology have completely different meanings to Taoism and to Buddhism. Large-scale confusion ensued. Gee, where have we heard that
But, one thread that seems to run through both before they met is the concept of separating emotion and cognitive thought from action, and of separating "self" from "being." In Taoism, it is becoming "One with the Tao"... a part of Nature and the universe not tied up in contemplating itself (and overcontemplating the world around it) and thus cluttering the Way. One must just "be." In Zen Buddhism and similar sects, this is similar to, if not the same as, the concept of "mu shin" (No Mind) - conditioning oneself to act correctly (see thread on "Old O Sensei video") without having to use conscious, verbal mental instruction that slows the process of initiation- to-execution of an action.
As relates to martial arts, this promotes, among other things, the ability to act in combat without pre-judging the situation, and to make in-the-moment decisions without mental clutter slowing down one's responses. It makes sense that some samurai-class folks would take on the practice of Zen to acquire pragmatic skills, if that's the only place such training could be accessed.