FastCGI App vs Apache Module - Drupal installation files and directories (except required) are not writable by the server.

In my hosting settings for "Php support" my web host gives the option to "run as Apache Module" or "run as FastCGI Application". If I set this to "run as Apache Module" and then run the security review module the site passes the "Drupal installation files and directories (except required) are not writable by the server" test. But if set to "run as FastCGl Application" it does not. The problem is that my host tells me for security reasons I should choose "run as FastCGI Applicaiton". Here is what they wrote -

The second drawback (of choosing "run as Apache Module") is a security issue. Created files will have the ‘nobody’ ownership. If a hacker finds an exploit in your PHP script, they could implement a file that has the same privileges as important system files that are also owned by ‘nobody’. This will give them the ability to modify files outside of that user’s account. This is really bad for anyone who does reselling or simply is hosting other person’s sites. You would not want one user to be able to affect another user.

My host and this module seem to have apposing views regarding which option is more secure. Any incite someone could give would be appreciated.