Answer
Check whether the user has the BrowseStarSchemaMetaData and ExecuteStarSchema activities granted — these two specific activities control access to Information Sources (star-schema-based) Data Sources in the Lobby Data Source Designer, separately from the broader set of system privileges the user otherwise has. Granting both resolves both symptoms: Information Sources becoming visible in the existing Data Sources list, and becoming selectable as an option when creating a new Data Source.