Not necessarily. *\;-)
The "ownership" rests in the Dennis Canon, passed ca. 1980 in order to staunch the tide of departing churches. Prior to the Canon the churches clearly owned their properties.
Questions have been raised about whether that Canon was properly passed; by canon law there were to be two votes on it and there is no apparently definitive record of the second. This has not been litigated yet, as far as I know -- at least there's no final resolution.
There are also situations (California, for example) where state law takes precedence and churches have left with property.
So there are cases where churches have left with, and cases where they have (for whatever reason) left without. Church ownership in TEC is not a study in black and white.
Roman Catholic Church ownership of Oxford University and Westminster Abbey and all of the old churches, convents and chantries of old England was absolutely black and white, but the new Anglican Church siezed it all anyway.
Grounds? According to the Anglicans of the day, the Church had lapsed into apostasy, particularly over the matter of simony.
Today, the Episcopalian Church endorses sodomy. God destroyed Sodom and Gemorrah over sodomy. (He never destroyed anyplace over simony).
So, where is the spiritual drive to do to the TEC what was done to Rome? The grounds are certainly better today.