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One possible explanation is that the site is using Forms Based Administration.

If so (as described by Outlook MVP Eric Legault in a newsgroup message),

"Client Integration is disabled by default for Authentication Providers that use FBA.

Turn this on, and Export to Spreadsheet, Open in Access and Connect to Outlook all reappear."

Thanks to Eric for posting this.

This

http://technet2.microsoft.com/Office/en-us/library/d3e0e0fc-77b6-4109-87d6-53ad088db01d1033.mspx?mfr=true

in the section headed "Client Integration" explains this setting and its effects.