Due to the way that different programs are integrated in Windows, sometimes other programs can show up as Windows Explorer processes and vice-versa. Some examples are Internet Explorer, WMP, ...
Additionally, when Windows Explorer is not configured to "Launch folder windows in a seperate process", this can happen whenever Internet Explorer is launched. "Launch Browser Windows in a Separate Process" Setting Is Not Available in Internet Explorer 5.01 or Internet Explorer 5.5
With this setting disabled, all instances of Internet Explorer and Windows Explorer that you start are run in the same process.
Also, some things that can result in Windows Explorer asking for internet access
When a new browser window is launched
When accessing bookmarks via Windows Explorer
If Active desktop is in use
When browsing network folders
If Windows Explorer is configured to view web content
If Windows Explorer is configured to launch folder windows in a separate process.
Also, check if the explorer.exe process is actually running from C:\Windows. If it is not, then it could be a virus infection.