How can an identity primary key index become fragmented?

From what I understand about index fragmentation, this should not be possible. The cases I have found in my databases are non-clustered.

Example:

ALTER TABLE [dbo].[ClaimLineInstitutional] ADD  CONSTRAINT [PK_ClaimLineInsitutional]  
PRIMARY KEY NONCLUSTERED 
(
    [ClaimLineInstitutionalID] ASC
)WITH (PAD_INDEX  = ON, STATISTICS_NORECOMPUTE  = OFF, SORT_IN_TEMPDB = OFF,   
IGNORE_DUP_KEY = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS  = ON, ALLOW_PAGE_LOCKS  = ON,    
FILLFACTOR = 100) ON [PRIMARY]

Update:

I am querying dm_db_index_physical_stats.avg_fragmentation_in_percent, so I believe it is physical fragmentation I am seeing.

Updates on data already there causes rows to be moved and forward pointers added

In this test, we can get 65% fragmentation on 115k densely packed rows

CREATE TABLE #FragTest (
    FragTestID int NOT NULL IDENTITY PRIMARY KEY,
    SomeString varchar(4100) NULL
    );

INSERT #FragTest (SomeString) VALUES ('a');
GO
INSERT #FragTest (SomeString)
    SELECT F1.SomeString FROM #FragTest F1 CROSS JOIN #FragTest F2;
GO 4
INSERT #FragTest (SomeString) SELECT F1.SomeString FROM #FragTest F1    
GO 6

SELECT COUNT(*) FROM #FragTest

SELECT object_id, avg_fragmentation_in_percent, page_count
FROM sys.dm_db_index_physical_stats(2, OBJECT_ID('tempdb..#FragTest'), NULL, NULL, NULL);

UPDATE #FragTest
SET SomeString = REPLICATE('b', 4100)
WHERE FragTestID < 10000 AND FragTestID % 3 = 0

SELECT object_id, avg_fragmentation_in_percent, page_count
FROM sys.dm_db_index_physical_stats(2, OBJECT_ID('tempdb..#FragTest'), NULL, NULL, NULL);

UPDATE #FragTest
SET SomeString = REPLICATE('c', 4100)
WHERE FragTestID < 10000 AND FragTestID % 3 = 1

SELECT object_id, avg_fragmentation_in_percent, page_count
FROM sys.dm_db_index_physical_stats(2, OBJECT_ID('tempdb..#FragTest'), NULL, NULL, NULL);

UPDATE #FragTest
SET SomeString = REPLICATE('d', 4100)
WHERE FragTestID < 10000 AND FragTestID % 3 = 2

SELECT object_id, avg_fragmentation_in_percent, page_count
FROM sys.dm_db_index_physical_stats(2, OBJECT_ID('tempdb..#FragTest'), NULL, NULL, NULL);

Edit, sorry, browser trouble

If you change the middle replicate to 2000 you get <5% at the end. This happens because there is free space from moved rows in the first update

StackExchange Database Administrators Q#7689, answer score: 8