...In 1763, George Washington and George William Fairfax were appointed church wardens with responsibility to contract for a new building. This was Washington’s last official act on behalf of this church after the parish was divided in 1765 and before work began...From the Truro Church website:
...Named after the Parish (now the Diocese) of Truro in England, Truro Parish was created by order of the Virginia House of Burgesses in 1732, some 10 years before Fairfax County itself came into existence. The father of George Washington, Augustine Washington, was a Truro vestryman and nominated the first regular rector of the parish in 1736. George Washington himself was appointed to the vestry in 1762...It appears both of these parishes are insinuating, if not directly claiming, that their roots go back to before the Revolutionary War, and both seem to be suggesting in their "histories" that George Washington was a member. In recent weeks, some of the articles in the secular press have affirmed this rendition of their history.
A new paper challenges the claims made by both of these parishes. The author of this report is Joan R. Gundersen, who holds a Ph.D. in American history from the University of Notre Dame. She has published extensively on the history of the church in Virginia, and is currently collaborating with Edward Bond on a new history of the Diocese of Virginia to be published by the Diocese of Virginia and the Virginia Magazine of History and Biography.
Here are a couple of sections from her research worth noting:
...There is a lot of confusion and misinformation being distributed concerning the actual history of these parishes, however. Neither is the direct descendant of a colonial parish. Neither can claim George Washington as a past member of its vestry or its congregation. Both are “new” church plants from the 1830s and 1840s. In most places in the United States, founding dates in the antebellum period would be quite old enough to justify a claim of being “historic,” but these two parishes have sought the additional aura associated with George Washington and our colonial past...The "confusion and misinformation" seems to be primarily derived from a misunderstanding of the term "colonial parish." It was not a specific congregation, as we would think the of the term "parish" referred to today. It was more of a geographical designation, somewhat like the way we might think of a "diocese":
...The colonial church in Virginia was an arm of the colonial government. The House of Burgesses divided the colony into parishes, and every square inch of Virginia was officially part of some parish. In order to make services accessible to the scattered, rural population of a parish, Virginia vestries usually constructed more than one place of worship in the parish. There might be a main church and several chapels of ease, or, sometimes, two more substantial buildings. The minister rotated services among the buildings, and lay clerks read Morning Prayer on the Sundays that the parson was at one of the other buildings. George Washington was on the vestry of the colonial parish of Truro, which for us might be the equivalent of serving on the Standing Committee. But he had no historical connection to the congregations that now claim the names of "The Falls Church" and "Truro Church":
The Falls Church is in possession of a restored colonial building that was once part of the colonial parish called Fairfax Parish. The site was originally in what was known as Truro Parish, but the building was constructed after the Virginia House of Burgesses divided Truro into two parishes in 1765.  Together, the colonial parishes of Fairfax and Truro covered the territory of Fairfax County.
There were no dioceses in the American colonies before the war. Afterwards, people who had been members of the Church of England began organizing as conventions, with lay and clergy participating. Eventually, these conventions became dioceses. Simultaneously, groups from the various states began organizing a national church, The Episcopal Church. The Diocese of Virginia retained its historic parish boundaries but allowed individual congregations within a parish to organize separately. Thus, in contemporary Virginia, there may be several parishes (i.e., distinct and independent “churches”) within the bounds of what was once a single colonial parish. More than one congregation within a parish may even own a colonial building...
...George Washington did have a lot to do with the colonial parishes we know as Fairfax and Truro. He served on the vestry of the colonial Truro Parish. The parish boundary line between Truro and Fairfax cut through his land. In 1765, he ran for the Truro vestry after the old Truro Parish was divided, and he was the third-highest vote getter. He occupied one of the 12 positions on that vestry until he resigned in 1784. Washington bought pews at three of the parish buildings in Fairfax County, Pohick, Payne’s, and Christ Church. His diary records attendance at all three of these buildings. However, neither the modern Truro Church nor The Falls Church can claim his regular attendance...Dr. Gunderson also provides us with an interesting final note regarding the Falls Church:
A final note is in order. In the 1830s when the Falls Church applied for admission as a parish, the constitution of the diocese included this provision as its Article XI:J.
Every parish within this Diocese shall be entitled to the entire benefit of this Convention, as soon as it shall have signified its ratification thereof, either in writing or by sending a Lay Delegate to the Convention; and such parish shall thereafter be benefitted and bound, equally with the other parishes in this Diocese, by every rule and canon which shall be framed, by any Convention acting under this Constitution for the government of this Church in ecclesiastical concerns. 
Parishes were thus bound by every rule and canon passed by any Convention of this Church. After 170 years these Virginia parishes are reneging on their promise.