No permission for select on table in a trigger function

I got the database "bikini-atoll" created using this PostgreSQL code:

CREATE TABLE TESTA (
        name character varying NOT NULL,
        age integer NOT NULL,
        PRIMARY KEY(name)
);

CREATE DOMAIN RANK AS character varying
CHECK (
    VALUE = 'bigmac' OR
    VALUE = 'smallmac'
);

CREATE TABLE TESTB (
        name character varying NOT NULL,
        rank character varying NOT NULL,
        PRIMARY KEY(name)
);

CREATE OR REPLACE VIEW TESTAB AS
SELECT * FROM (TESTA
        JOIN
           TESTB
           ON TESTA.name = TESTB.name);


CREATE OR REPLACE RULE TESTAB_INSERT 
AS ON INSERT TO TESTAB
DO INSTEAD (
    INSERT INTO TESTA (name,age) VALUES (NEW.name,NEW.age);
        INSERT INTO TESTB (name,rank) VALUES (NEW.name,NEW.rank);
        )

CREATE OR REPLACE FUNCTION testRankToAge() RETURNS TRIGGER AS $$
DECLARE
    ageRes integer;
BEGIN
    SELECT AGE INTO ageRes
    FROM TESTA
    WHERE name = NEW.name;

    IF (ageRes < 42) AND (NEW.rank = 'bigmac')
    THEN
    RAISE EXCEPTION 'YOU CANNOT BE BIGMAC AT THAT AGE';
    END IF;
END
$$ LANGUAGE plpgsql;

CREATE OR REPLACE TRIGGER rankToAgeTrigger
AFTER INSERT
ON TESTB
    FOR EACH ROW
    EXECUTE PROCEDURE testRankToAge();

DROP ROLE IF EXISTS testUser;
CREATE ROLE testUser WITH PASSWORD '123456' LOGIN;

GRANT INSERT ON TESTAB TO testUser;

Now I want my (Common-LISP) program to do a simple insert:

(clsql:file-enable-sql-reader-syntax)

(clsql-sys:with-database (db (list "localhost" "bikini-atoll" "testuser" "123456") :database-type :postgresql)
  (clsql-sys:insert-records :into [TESTAB]
                :attributes '([NAME] [AGE] [RANK])
                :values '("sir" 44 "bigmac")
                :database db))

which basically is an:

INSERT INTO TESTAB (NAME,AGE,RANK) VALUES ('sir',44,'bigmac');

as user testuser (I doubt that this is a program language specific problem, and more some sort of bad database/trigger design on my part).

But the (unexpected) result is:

Error 42501 / FEHLER:  no permission for relation testa
CONTEXT:  SQL-COMMAND „SELECT AGE              FROM TESTA
    WHERE name = NEW.name“
PL/pgSQL-Funktion testranktoage() LINE 5 AT SQL-Command
  has occurred.

which would suggest that testuser would also need SELECT permissions on any table a trigger might do stuff on, which seems a bit odd as I thought that one of the main reasons for views is to limit/filter the access of a user to tables, which would the opposite of granting any SELECT needed by a consistency trigger.

How to I fix/prevent this dawning permission havoc?

which would suggest that testuser would also need SELECT permissions on any table a trigger might do stuff on

That's exactly correct. Except, there are ways around it. Like a SECURITY DEFINER trigger function.

Here is a closely related answer with detailed instructions:
Is there a way to disable updates/deletes but still allow triggers to perform them?