从Laravel存储下载而不将整个文件加载到内存中

我正在使用Laravel Storage，我想为用户提供一些文件（大于内存限制）。我的代码是从SO的一篇文章中获得灵感的，它是这样的：

$fs = Storage::getDriver();
$stream = $fs->readStream($file->path);

return response()->stream(
    function() use($stream) {
        fpassthru($stream);
    }, 
    200,
    [
        'Content-Type' => $file->mime,
        'Content-disposition' => 'attachment; filename="'.$file->original_name.'"',
    ]);

不幸的是，我遇到大文件错误：

[2016-04-21 13:37:13] production.ERROR: exception 'Symfony\Component\Debug\Exception\FatalErrorException' with message 'Allowed memory size of 134217728 bytes exhausted (tried to allocate 201740288 bytes)' in /path/app/Http/Controllers/FileController.php:131
Stack trace:
#0 /path/vendor/laravel/framework/src/Illuminate/Foundation/Bootstrap/HandleExceptions.php(133): Symfony\Component\Debug\Exception\FatalErrorException->__construct()
#1 /path/vendor/laravel/framework/src/Illuminate/Foundation/Bootstrap/HandleExceptions.php(118): Illuminate\Foundation\Bootstrap\HandleExceptions->fatalExceptionFromError()
#2 /path/vendor/laravel/framework/src/Illuminate/Foundation/Bootstrap/HandleExceptions.php(0): Illuminate\Foundation\Bootstrap\HandleExceptions->handleShutdown()
#3 /path/app/Http/Controllers/FileController.php(131): fpassthru()
#4 /path/vendor/symfony/http-foundation/StreamedResponse.php(95): App\Http\Controllers\FileController->App\Http\Controllers\{closure}()
#5 /path/vendor/symfony/http-foundation/StreamedResponse.php(95): call_user_func:{/path/vendor/symfony/http-foundation/StreamedResponse.php:95}()
#6 /path/vendor/symfony/http-foundation/Response.php(370): Symfony\Component\HttpFoundation\StreamedResponse->sendContent()
#7 /path/public/index.php(56): Symfony\Component\HttpFoundation\Response->send()
#8 /path/public/index.php(0): {main}()
#9 {main}  

似乎它试图将所有文件加载到内存中。我原以为使用stream和passthru不会做到这一点……我的代码中缺少某些内容吗？我是否必须以某种方式指定块大小或什么？

我使用的版本是Laravel 5.1和PHP 5.6。