Is there any reasonable way to determine what executed a query?
Use SQL Auditing to track from where those statements are coming.

Set-AzureRmSqlDatabaseAuditing -ResourceGroupName "resourceGroup"
 -ServerName "SQL Server Name" -DatabaseName "AdventureWorksLT"  
 -StorageAccountName "storageAccount" 
-AuditActionGroup "SUCCESSFUL_DATABASE_AUTHENTICATION_GROUP", "FAILED_DATABASE_AUTHENTICATION_GROUP", "BATCH_COMPLETED_GROUP" 
 -AuditAction "UPDATE ON database::[AdventureWorksLT] BY [public]"  
 -RetentionInDays 60


A sample audit record for the BATCH_COMPLETED_GROUP will show the following information:



As you can see it gives you the IP address, the principal name and the application name that generated the SQL statement.