SQLSTATE[HY093]: Invalid parameter number: no parameters were bound, but parameters are provided

I'm building a database object that joins the PDO object with the PDOStatement object in order for chaining to be available. Basically I just put the methods I most frequently use, but bindParam is giving me a hard time.

private $stmt = null;

...

public function prepare($statement,array $driver_options = array()) {
    if($this->stmt) throw new \Exception('PDO Statement already prepared, no override!');
    $this->stmt = parent::prepare($statement, $driver_options);
    return $this;
}

public function bindParam($place, &$val, $dataType){
    if(!$this->stmt) throw new \Exception('PDO Statement is empty');
    $this->stmt->bindParam($place, $val, $dataType);
    return $this;
}

public function execute(array $params = array()){
    if(!$this->stmt) throw new \Exception('PDO Statement is empty');
    $this->stmt->execute($params);
    return $this;
}

public function fetchAll($pdoFetchType){
    if(!$this->stmt) throw new \Exception('PDO Statement is empty');
    return $this->stmt->fetchAll($pdoFetchType);
}

...

public function getStmt(){
    return $this->stmt;
}

public function clearStmt(){
    $this->stmt = null;
}

I get the error, from the title, in this code:

$i = 0;
$db->prepare('SELECT * FROM users LIMIT ?,1')->bindParam(1, $i, \PDO::PARAM_INT);
while($row = $db->execute()->fetchAll(\PDO::FETCH_ASSOC)){
    echo "<pre>".print_r($row, true)."</pre>";
    $i++;
}

Basically what I found out about this error is that it occurs when provided variables in bindParam are null, but $i is clearly not null. Can you help me out?

EDIT: Also running

var_dump($this->stmt->bindParam($place, $val, $dataType));

in the bindParam method returns TRUE. From the manual:

Return Values

Returns TRUE on success or FALSE on failure.

It's succeeding but not binding the parameter ??? I feel my brain is going to explode soon.