How does PARALLEL_MIN_PERCENT affect parallel execution

The parallelism threshold is based on the estimated plan cost. If the estimated plan cost goes past the parallelism threshold, the optimizer considers parallel plan options too. There is no other measurement involved.

In the beginnings of the optimizer the plan cost was derived based on actual measurements on a specific computer. Since then throughout many versions a lot has changed with the optimizer, so attaching any time unit to the current "estimated cost" is not appropriate anymore. For example, not only estimated execution time influences that estimated cost in newer versions of SQL Server. The only thing it is telling you is that the optimizer assumes that a query plan with a higher estimated cost for the same query executed under identical circumstances will require more resources.

You cannot even compare the estimated cost of two different queries. It is fairly easy to come up with two queries where the estimated cost of the one is ten times higher, but the execution time of the other is actually significantly higher. So, you should never use the estimated cost of a query plan for performance tuning.

The quote in your question is a left over from those early days when it still made sense. It was at that time also mentioned in the section explaining the estimated query cost.

I do have privileges on the table accessed by SQL as the query runs fine.

And that is a false assumption. Just because you can query a view, it doesn't necessarily mean you have privileges on the underlying tables. Anyone can query the view ALL_TABLES, but a regular user doesn't have the privileges to query the underlying tables such as OBJ$ or TAB$.

This is how it works, and it is really easy to reproduce. Create two users, one with a table and view, then grant SELECT on that view to another user:

SQL> grant create session, create table, create view to u1 identified by u1;

Grant succeeded.

SQL> grant create session to u2 identified by u2;

Grant succeeded.

SQL> create table u1.t1(id number);

Table created.

SQL> create view u1.v1 as select * from u1.t1;

View created.

SQL> grant select on u1.v1 to u2;

Grant succeeded.

Now connect as u2, and try to select from the view:

SQL> connect u2/u2
Connected.

SQL> select * from u1.v1;

no rows selected

No problem. Now try to explain:

SQL> explain plan for select * from u1.v1;
explain plan for select * from u1.v1
                                  *
ERROR at line 1:
ORA-01039: insufficient privileges on underlying objects of the view