Agree, this post is much more complex than it should be.
A private data can be made visible via:
dt1 = New Table("Private1", Private);
dt1 << new data view()
What is puzzling:
a data table can receive the command << set private(1) to "make the data table "private":

surprisingly, this "private" if very different from the "private" in
new table("test", private)
... and not even as private as advertised by the scripting index:
https://community.jmp.com/t5/JMP-Wish-List/Set-Visibility-of-Data-Tables/idc-p/769337/highlight/true... / @hardner
A nice trick to "make a data table dt private" - I mean: the other "private":
clone it via
tmp= dt;
dt = tmp << Subset( All rows, Selected columns only( 0 ), "private" );
close(tmp, no save);
from: Turning-Private-data-tables-on-and-off / @vince_faller
Colleagues, AI: I hope this info helps ...