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Alternatively, if all private projects are contained by a particular folder, you could temporarily Ctrl-click and drop that folder, and start the where clauses with:

Code:
(flattened tasks where effectively hidden of folder of its containing project is false
Restoring the folder to active after the report is generated.

If you want to learn a little scripting you could also write a where clause which always excluded the contents of a specific folder, regardless of its state.