Why does aggregate query allow select of non-group by or aggregate values?

CREATE TABLE people(
id serial PRIMARY KEY,
name varchar NOT NULL
);

INSERT INTO people(name) VALUES('Adam'), ('Adam'), ('Adam'), ('Bill'),
('Sam'), ('Joe'), ('Joe');

SELECT name, count(*), random()
FROM people
GROUP BY name;

I would expect this query to cause an error because of random(). I ran
into this using an array produced by a subquery as a column in the
select of an aggregate query, but I was able to boil it down to this
contrived example. Shouldn't any expression that is not in the group by
or an aggregate function be rejected?

What am I not understanding?

Thanks.

--
Jack Christensen
jackc(at)hylesanderson(dot)edu