Strange - RequiresNew in the inner (Logging) TransactionScope should work.
In the below nested transaction, TransactionScopeOption.Suppress or TransactionScopeOption.RequiresNew both work for me - the inner transaction is committed (Dal2.x), and the outer one aborted (Dal1.x).
    try
    {
        using (TransactionScope tsOuter = new TransactionScope(TransactionScopeOption.Required))
        {
            DAL1.Txn1();
            using (TransactionScope tsLogging = new TransactionScope(TransactionScopeOption.Suppress))
            {
                DAL2.Txn2();
                tsLogging.Complete();
            }
            throw new Exception("Big Hairy Exception");
        }
    }
    catch (Exception ex)
    {
        MessageBox.Show(ex.Message);
    }
Edit : Mixing TransactionScope and explicit T-SQL transactions is to be avoided - this is stated in the same link you've referenced viz http://msdn.microsoft.com/en-us/library/ms973865.aspx, quoted below
TransactionScopes manage transaction escalation quite intelligently - they will use the (e.g. DTC will only be used if the transactions span multiple databases or resources - e.g. SQL and MSMQ). They also work with the SQL 2005+ Lightweight transactions, so multiple connections to the same database will also be managed within a transaction without the overheads of DTC.
IMHO the decision as to whether to use Suppress vs RequiresNew will depend on whether you need to do your auditing within a transaction at all - RequiresNew for an isolated txn, vs Suppress for none.
  When using System.Transactions,
  applications should not directly
  utilize transactional programming
  interfaces on resource managers—for
  example the T-SQL BEGIN TRANSACTION or
  COMMIT TRANSACTION verbs, or the
  MessageQueueTransaction() object in
  System.Messaging namespace, when
  dealing with MSMQ. Those mechanisms
  would bypass the distributed
  transaction management handled by
  System.Transactions, and combining the
  use of System.Transactions with these
  resource manager "internal"
  transactions will lead to inconsistent
  results .... Never mix the two