It does better when, for example, you have a field called 'id' in both tables.
SELECT
*
FROM table1
JOIN table2
ON table2.rel_id = table1.id
will use one of the 'id' field from table1 or table2 (depending on the join type).
SELECT
table1.*
FROM table1
JOIN table2
ON table2.rel_id = table1.id
will use the 'id' field of table1 and does not include data from table2.
But I agree with your other arguments.