I just had a problem deleting system files. Every time I tried to delete a file it told me it was open (see the attachment DeleteFile.png). Closing the project didn't work either then you get the Delete Grayed out (see attachment DeleteFileGrayedOut.png). So I asked PTC support (Stefan) for some help and here is the process for deleting a system file:
Open PTC WCS
Open the system file you want to delete
Go to File > Close (NOT Close Project which is what I was doing)
The start page is now displayed (but although you can't see it the project is still open so you can access files within it)
Use the Project Navigator to select and delete the system file.