Aren't two writes required to update a clustered index record
I think the problem here is a difference in terminology.

The "number of writes" that's usually referred to is the number of object accesses, rather than the number of pages that get touched by the physical operation.

The reason why that's usually used as a metric in discussion is because it's a more "stable" and meaningful number to talk about. As we're getting into here, the number of pages touched by an INSERT statement for even a single row depends on many factors, so it's not a very useful quantity outside your own environment and situation.



The one thing I would pick at from the article quote is this (emphasis mine):


  One write for inserting the row, and one write for updating the non-clustered index.


This may be confusing. Inserting a row into the base table would involve an insert to the base table, and also an insert into each nonclustered index (ignoring special index features), not an update.


  So if a record has to be updated, say the value 1 has to be updated to 7, won't the update need to be applied to both the key in the clustered index top node (this may, in cases, cause a re-structuring of the entire structure) and the corresponding value in the record in the leaf-page?


Yes, assuming the column that was updated is in the index key. However, this is still a single object access, and hence a "single write."