ONLY_FULL_GROUP_BY silently bypassed for outer-correlated fields inside aggregate

SET sql_mode='ONLY_FULL_GROUP_BY';

CREATE TABLE t0 (a INT, b INT, c INT);

CREATE TABLE t1 (b INT);

INSERT INTO t0 VALUES (1,10,100),(1,20,200),(2,30,300);

INSERT INTO t1 VALUES (1000);

#here error as expected:

--error 1055

SELECT (SELECT sum(t0.b + t1.b) FROM t1) AS s, t0.c FROM t0 GROUP BY t0.a;

#here error is also expected:

SELECT t0.a, (SELECT sum(t0.b + t1.b) FROM t1) AS s FROM t0 GROUP BY t0.a;

SELECT t0.a, (SELECT any_value(t0.b + t1.b) FROM t1) AS s FROM t0 GROUP BY t0.a;

DROP TABLE t0, t1;

SET sql_mode=DEFAULT;

query 'SELECT t0.a, (SELECT sum(t0.b + t1.b) FROM t1) AS s FROM t0 GROUP BY t0.a' failed: ER_WRONG_FIELD_WITH_GROUP (1055): 'test.t0.b' isn't in GROUP BY