A little more reading revealed that the internal database snapshot is implemented as an alternate stream of the live database file. And also that I have no control over where it's created, so it can cause a nearly full drive to fill up during a CHECKDB (the original reason for his original article).
I had never heard of an alternate stream before, but I did find a couple pretty good explanations, that I won't cover here, other than to mention that it's a feature of NTFS and allows multiple data streams to be stored within a single file (the second link has downloadable source-code for utilities that manipulate alternate data streams, if you really want to get down in the weeds).
I wanted to see one of these alternate streams in action myself, and discovered that you can view a file's alternate streams by using the /R switch of the DIR command. Here is DBCC CHECKDB in action, complete with a peek at the alternate steam in the file system.
I'm using the following command to provide directory listings for the AdventureWorks database:
This shows the AdventureWorks_Data.mdf file:
Now run dbcc checkdb('AdventureWorks') and, while that is still running, kick off the DIR command from a separate SSMS window. This shows the AdventureWorks_Data.mdf file and the alternate stream that is used for the internal database snapshot: