How interesting.
Database changed
mysql> CREATE TABLE t (c TIMESTAMP) ENGINE=InnoDB;
Query OK, 0 rows affected (0.06 sec)
mysql> insert into t values (1);
Query OK, 1 row affected, 1 warning (0.03 sec)
mysql> show warnings;
+---------+------+----------------------------------------+
| Level | Code | Message |
+---------+------+----------------------------------------+
| Warning | 1265 | Data truncated for column 'c' at row 1 |
+---------+------+----------------------------------------+
1 row in set (0.00 sec)
mysql> select * from t;
+---------------------+
| c |
+---------------------+
| 0000-00-00 00:00:00 |
+---------------------+
1 row in set (0.00 sec)
mysql> select * from t where c = 1;
Empty set, 1 warning (0.00 sec)
mysql> show warnings;
+---------+------+-------------------------------------------------------+
| Level | Code | Message |
+---------+------+-------------------------------------------------------+
| Warning | 1292 | Incorrect datetime value: '1' for column 'c' at row 1 |
+---------+------+-------------------------------------------------------+
1 row in set (0.00 sec)