Thanks for the tip, but this doesn't seem to be my issue. I am already accessing the plugin from an "Administrator" account. :(
I thought it might be related to downloading the files to a Mac and then uploading them (I know this causes permissions problems on my LAN with Unix boxes). So I tried downloading to a WinXP machine and FTPing from there, but I have the same result.
One thing that occurred to me is that this WP install is on a server that I'm accessing through a particular domain that resolves to the proper IP through my local hosts file. So anyone who tries to access the site through this domain without having first edited their local host file to resolve to the proper IP will see a completely different site.
I can't see how this would cause a problem myself, but who knows?