That is certainly interesting, and something that gets little attention in U.S. history courses.
However, there is some debate about what exactly happened. In any case, Washington was acting on the orders of the colonial government on behalf of the British empire, and this after the French had already entered disputed territory with the intention to hold it. If one looks at the actions at Jumonville Glen itself, the chief issue - what might have been the murder of the French commander - appears from two separate sources to have been the spontaneous work of Washington's Mingo ally, Tanacharison. There is also some question of which side fired the first shot.
So although this particular war began in the colonies, it is perhaps a bit much to claim that the English colonists were responsible for it - especially in the context of centuries of enmity between Britain and France which predated the discovery of America.