ArcMap 10.6.1 and Pro 2.2.0
Error "Could not analyze datasets DatabaseName.DataOwner.FeatureClass.
(You might not have sufficient permissions.)"
This occurs only on datasets that are using Esri Binary spatial type.
However, if the statistics are checked in the database they have been updated.
Seems to be a "false error"
Work around, use Geometry spatial type or use a different client to run Analyze Datasets tool.
Runs fine using ArcMap 10.5.0