WMI "installed" query different from add/remove programs list?

Besides the most commonly known registry key for installed programs:

HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Uninstall

wmic command and the add/remove programs also query another registry key:

HKEY_CLASSES_ROOT\Installer\Products

Software name shown in the list is read from the Value of a Data entry within this key called: ProductName

Removing the registry key for a certain product from both of the above locations will keep it from showing in the add/remove programs list. This is not a method to uninstall programs, it will just remove the entry from what's known to windows as installed software.

Since, by using this method you would lose the chance of using the Remove button from the add/remove list to cleanly remove the software from your system; it's recommended to export registry keys to a file before you delete them. In future, if you decided to bring that item back to the list, you would simply run the registry file you stored.

All that Add/Remove Programs is really doing is reading this Registry key:

HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Uninstall

I believe your syntax is using the Win32_Product Class in WMI. One cause is that this class only displays products installed using Windows Installer (See Here). The Uninstall Registry Key is your best bet.

HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Uninstall HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Uninstall

UPDATE FOR COMMENTS:

The Uninstall Registry Key is the standard place to list what is installed and what isn't installed. It is the location that the Add/Remove Programs list will use to populate the list of applications. I'm sure that there are applications that don't list themselves in this location. In that case you'd have to resort to another cruder method such as searching the Program Files directory or looking in the Start Menu Programs List. Both of those ways are definitely not ideal.

In my opinion, looking at the registry key is the best method.