Auto Created Statistics And Missing Statistics

Hello group.

I have an issue, which has bothered me for a while now:

I'm wondering why the column statistics, which SQL Server wants me to
create, if I turn off auto-created statistics, are so important to the
optimizer?

Example: from Northwind (with auto create stats off), I do the following:

SELECT * FROM Customers WHERE Country = 'Sweden'

My query plan show a clustered index scan, which is expected - no index
exists for Country. BUT, the query plan also shows, that the optimizer is
missing a statistic on Country, which tells me, that the optimizer would
benefit from knowing this.

I cannot see why? (and I've been trying for a while now).

If I create the missing statistics, nothing happens in the query plan (and
why should it?). I could understand it, if the optimizer suggested an index
on Country - this would make sense, but if creating the missing index, query
analyzer creates the statistics with an empty index, which seems to me to be
less than usable.

I've been thinking long and hard about this, but haven't been able to reach
a conclusion :) It has some relevance to my work, because allowing the
optimizer to create missing statistics limits my options for designing
indexes (e.g. covering) for some rather wide tables, so I'm thinking why not
turn it off altogether. But I would like to know the consequences - hope
somebody has already delved into this, and knows a good explanation.

Rgds
Jesper