For better or for worse, the Episcopal Church structure is such that each diocese essentially owns the churches within that diocese, not the congregations. The same is true for the Methodist and I believe the Roman Catholic Churches. There are several other denominations where the real property is owned by a large, regional, or statewide body rather than the local congregations.
Some Dioceses have let departing congregations purchase the relevant church building, particularly where the building is heavily encumbered with mortgages. I believe this happened recently in Raleigh, NC.
On the other hand, the congregations of the Baptists and the Churches of Christ and other denominations own their own church buildings.
If you are thinking of making a substantial contribution towards church improvements, you might want to take a look at what body actually owns it if these types of issues concern you.
There was discussion a while back on Brit Hume's program on FNC about one of these parishes in Northern Virginia, which Fred Barnes is a member of...apparently the local parish paid for everything they have, but it's probably one the diocese is trying to confiscate.
Some of the churches/parishes in question predate the formation of the denomination which is now called the TEC. The other parishes are generally daughter churches of these early parishes. TEC can claim it owns the church properties outright, but it is no foregone conclusion.
I am certain that rule was instituted with exactly this sort of conflict in mind.