Use functions: uc_file_user_downloads function and theme function
If it is drupal 6 in order to print the  table you can simply do print uc_file_user_downloads($account); ,this function will internally call the theme function theme_uc_file_user_downloads

What you are trying in your code is combination of both.So in drupal 6 try witih the following code.

global $user;
print uc_file_user_downloads($user);


In drupal 7 the function uc_file_user_downloads($account); returns array unlike html in drupal 6. So try the following with drupal 7

module_load_include('inc', 'uc_file', 'uc_file.pages');
global $user;
$table = uc_file_user_downloads($user);
print drupal_render($table['downloads']);