CCleaner Leaves Files Showing Trail of Web Activity

Why doesn't CCleaner delete the content of the following files?:

C:\Documents and Settings\USER NAME\Local Settings\Application Data\Google\Chrome\User Data\Default\History

and

C:\Documents and Settings\USER NAME\Local Settings\Application Data\Google\Chrome\User Data\Default\Favicons

These clearly show browser history in detail or in a general sense in the case of the Favicons.

Currently a bug is in ccleaner with the latest chrome, this may be the issue here.