Nah, the warning comes from the extended attribute on the application folder/zip. It has nothing to do with the log.
You can disable the warning by a command line:
xattr -d com.apple.quarantine <path_to_your_program>
You can disable the warning by a command line:
xattr -d com.apple.quarantine <path_to_your_program>
Furthermore, even once a file is out of quarantine, the Get Info dialog can still tell you where it was downloaded from, precisely because of this database.