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Apologies for not replying sooner.
I have an iMac setup as a TV in my bedroom and upon first launch or a full restart a password was required to allow the Remote Buddy AJAX Remote keychain item in the Login keychains to be accessed by Remote Buddy.
There are no special items that were setup within the iMac, it has a standard install with the first account as an administrator account, the second account is non administrator which is the default login account. When the iMac reboots it is set to enter this account (TV) and as this has no passwords set should not cause any app that is set to 'Open at Login' any problems.
To confirm Remote Buddy was installed following the installation instructions, again no special configuration has been performed to the app at all, it is running as standard, yet on two computers at home the app has the same keychain in the login items, called Remote 'Buddy AJAX Remote'.
To follow your advice I have moved the Remote Buddy AJAX Remote keychain item from the Login to the System Keychain and this seems to have happily done the trick. :)
It would be useful to know what the item in the Keychain is used for, as you noted previously there should be no need for the keychain but on two macs there is an entry!