Reading that I would recommend the hacked module
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drupal.org...]
Basically, it verifies that your code base matches the code base on Drupal.org for Drupal and your modules. Obviously if you've hacked a module yourself, that will get flagged. But unless you've applied a known patch, you shouldn't be hacking anything in most cases (you should be plugging in and overriding). So hacked! should let you know if you've been compromised.
If you have a dev -> test -> live workflow, you can update your dev version, run Hacked! and verify the codebase, then do a git push to test and live.
I'm not sure what they mean by "manually" download updates. Most people are going to use drush or git to pull updates. Is that manual? It should be the same source.