Only a guess here.

The Touro is the oldest synagogue building in the US, but it is not the oldest continuously operating congregation. Shearith Israel has been in operation since 1654. My guess would be Shearith Israel bought or inherited (both buildings are originally Sephardic) and preserved the Touro for the 200+/- odd years before the current residency.  These stories, while sad, usually have an economic basis. Leasing the building for $1 is noble, until inflation occurs. This brings Barbara Sloans statement into focus who pays for the "extensive repairs in the last decade or two", and how are those repairs performed under whose review? The owner, the tenants?

Bottom line, I don't know the whole story. I wish all parties well.
Jonathan Wexler