Cannot delete files from Favorites folder under user profile in Windows Server 2003

This was the strangest and the most annoying thing today. I tried to delete a user profile from Windows 2003 Server only to get Access Denied error while deleting some .url shortcuts under Favorites folder. What's more, I was logged in under Administrator account, the Properties dialog for the file did not show the Security tab and I got same Access Denied when trying to change the ownership or permissions from the parent folder. After poking around on the internet, I stopped the Indexing Service and then those files disappeared and I was able to remove the profile. I do not have time nor inclination to figure out exactly what was going on.