ANSI SQL does not guarantee rows in any order, so an ordering statement is required.
Ever since the advent of worker processes (ASE 11.5) ASE does not guarantee rows returned in sorted order unless an ORDER BY is used. This became more apparent when DOL tables were introduced, per Bret's answer.
Historically, ASE would table scan and return results in clustered index order without any additional sorts in a table scan, so older code was written to avoid the sort by eliminating the ORDER BY, as it was a redundant operation. With the current and recent changes to ASE and the optimizer, that is not guaranteed unless you provide the sorting instructions.
ASE will still put the rows in strict clustered order on APL tables, but for DOL tables you must rebuild/reorg the table to ensure it is in clustered index order. As the application should not be aware of the underlying locking mechanism of the table, the only guarantee of ordered-ness is what you specify in the SQL.
The documentation quote you reference comes from the Transact SQL Users Guide in the documentation (under Using clustered or noclustered indexes) and does not state the table type. However, the definition of an APL clustered index is "The bottom or leaf level of a clustered index contains the actual data pages of the table". This is not true for a DOL table.
You may have found a documentation error.
Chris