MySQL: Sorting by primary key or index?

Question

MySQL

Started optimizing the database. Approached to studying of a question of indexes in MySQL.
As you know, the capacity of queries is determined by the EXPLAIN command.
There is a table ID MEMBER VIP
Query:
SELECT * FROM vip WHERE member='1'
The explain command shows rows - 8500 . That is, to execute the request, you have to check all the rows.
It turns out that I need to set an index on the member field and the problem will be solved.
But! Why with such a request

SELECT * FROM vip WHERE member='1' ORDER BY id DESC LIMIT 0,1

The explain command shows rows - 1 . I mean, everything is great. The note was found immediately.
ID in this case is a PRIMARY KEY, that is, the main index.
It turns out that for unique values, just sorting the field by the primary key is enough?
For non-unique, of course, it will not work, since LIMIT is unknown.
Or do I still misunderstand something and the index on the member field is required in this case?
Thanks in advance for your time.

Answer 1

Each leaf of the btree index contains the primary key value for a particular value. (sorry for the tautology)