Having installed a 64 bit version of Java and HP Diagnostics on a Windows Server 2008 64 bit platform, an attempt to access the HP Diagnostics User Interface using the default Internet Explorer browser on the same platform results in a "Security Warning" popup that seeks permission to install the "Java SE Runtime Environment 6".
The default Internet Explorer browser on a Windows Server 2008 64 bit platform is the 32 bit version which is not compatible with a 64 bit Java version. Hence the browser prompts to install a 32 bit Java version.
To avoid the need to install a 32 bit version of Java, use the 64 bit version of Internet Explorer instead. To identify which Internet Explorer version is in use, open the "About Internet Explorer" dialog (Help->About Internet Explorer). The 64 bit version of Internet Explorer will display the text "64-bit Edition" beside the version details.