Transact SQL :: Any Reason For Difference In Order Of Columns Between Index Of Constraint And Its Statistics Definition?

I am really puzzled by an apparent difference between table index key column order and its statistics order. I was under understanding that index statistics mirror index definition. However, in my db 2470 index ordinal definitions match statistics definition but 66 do not. I also can reproduce such discrepancy in 2008 R2, 2012 and 2014.

As per definition,

stats_column_id
int

1-based ordinal within set of stats columns

This script duplicates this for me.

BEGIN TRAN
GO
use tempdb
GO
CREATE TABLE [dbo].[ItemProperties](
[itmID] [int] NOT NULL,
[cpID] [smallint] NOT NULL,
[ipuID] [tinyint] NOT NULL,

[Code] ....

The result I get is this:

object_id       stats_name                                     
stats_column_list
1525580473 PK_ItemProperties_itmID_ipuID_cpID itmID,  cpID,  ipuID,

and

object_id      index_name                                     
index_column_list
1525580473 PK_ItemProperties_itmID_ipuID_cpID itmID,  ipuID,  cpID,

Also a query I used to discover this in my db is:

WITH stat AS
(
SELECT
s.object_id
,s.name as stats_name
,(
SELECT
c.name + ', ' as [data()]
FROM sys.stats_columns as sc

[Code] .....