Although I am not using Total Commander,
this thread held the answer to my question.
My original thought about a "virtual" folder isn't far from the truth:
On a Windows 64-bit operating system (which the three installations of W7 used in investigations all are), any request by a 32-bit application (which the web browsers in use all are) to save a file in System32 will instead be invisibly redirected to SysWOW64. The file will still appear to be in System32 when queried by a 32 bit application, but in fact it isn't there; it's in SysWOW64. In relational database terms, the 32-bit application is behaving as if querying a view that joins two tables rather than directly acting on an underlying table or tables.
Sure enough, if I open C: \Windows\SysWOW64 using Windows Explorer (which is 64-bit of course on a 64-bit version of Windows), I see the files even though they were saved to C: \Windows\System 32.