While there are a number of reasons that viewing a report can result in an "Insufficient Privileges" error, in Experience Cloud sites the most common cause is that the External Organization-Wide Defaults of one or more involved objects aren't set to "Private".
Report Summary components have a "Report Id" setting allowing Administrators to set the component to display a single report regardless of which report is linked. To resolve this issue, complete the following steps:
{!recordId}.Log in as the site user and open the filters panel on the report to confirm that the user can see all of its filters. If a filter is missing, it is because the site user doesn't have access to the field. To resolve the issue, grant the user at least read access to the field by editing their profile or by assigning them a permission set.
As with filters, a column or grouping doesn't appear in a report if the running user doesn't have access to the underlying field. To resolve, give the user at least read access to the field via their profile or a permission set.
Report charts in Experience Builder sites — whether viewed on the report's run page or as an embedded component — function as embedded report charts do in core Salesforce. This means that the groupings on the report chart appear in the order they're set on the source report's groupings and not necessarily the report chart.
Site users may experience an issue where clicking anything in the Export Report or Save As screens makes it appear as if they're interacting with the report run page. This happens when a custom theme has been applied to the Report Detail page and its styling has not accounted for overlapping.
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