column "b" is of type X but expression is of type text

A third party application we use generates SQL queries. Here is query it
generated that broke today and for which I have a hard time arguing that
the postgres behavior is correct (minimally the error message is confusing):

=# create temporary table foo (b double precision );
CREATE TABLE
Time: 40.368 ms
=# insert into foo select min(NULL);
ERROR: column "b" is of type double precision but expression is of type
text
LINE 1: insert into foo select min(NULL);
^
HINT: You will need to rewrite or cast the expression.

So why does min(NULL) have type text? According to the docs it has the
type of the input. The value is itself NULL which is a valid member of all
types in SQL isn't it?

So what is going on?

Thanks,

Bene