How can I force an app install in App Store, or otherwise get App Store in a consistent state?

I've recently reinstalled OS X Mountain Lion on a laptop (completely and thoroughly erased the partitions of the previous installation), and on this freshly created system, after I sign in to the App Store (to download previous purchases), the system behaves as if packages are already installed - which they are not!

Under the Purchases tab, packages (such as Xcode or other previous purchases) are showing with a greyed out "INSTALLED" button on the right. Other packages (which have not been installed) are showing with a (pressable) button of "UPDATE". (For example, iPhoto has a newer version in Mavericks; it seems always possible to click on UPDATE and be prompted to install the latest version for Mountain Lion -- even though that process can be infinitely repeated). But iPhoto (along with any other packages) has not been installed to the host yet. /Applications/iPhoto.app and any others are not showing at all on the system, but App Store still believes that they're installed already (preventing a real install, or pretending that an upgrade is an upgrade and not an install). There are some packages which DO say "INSTALL". Those are the ones that I have never installed before on the laptop. So it appears to be possible to still install some packages - but that's the set that I do not want to install. So for example, now I can't seem to install Xcode or iPhoto or any other previously purchased applications. It seems pretty clear that there are some bugs here. But I am concerned about the source of the association - how is OS X determining that THOSE packages are "installed already", but others are not? Is the upstream App Store server keeping track of machine ID to make this determination? I heard at one point that App Store uses Spotlight internally - is it somehow querying that? Finally I wanted to confirm that this is really a complete reinstall. I set /dev/zero to the first few sectors of the raw hard drive in order to ensure that I could make a few partiiton table, and when I then reinstalled the system, I chose a different partition arrangement. I have no other drives connected. So it's truly a reinstall of the OS from scratch, and at the moment I can't see a clear way to install apps! I also had killed the App Store agent running in the background, moved away App Store related files in ~/Library/Caches/ and started again. Yet I get the exact same response. This is concerning from a privacy perspective too. Suppose the App Store server is encoding the list of installed packages and associating it with the host and then perhaps I sell the laptop. Now the list of apps may be available to a new user of the laptop. But it may only show if the same Apple ID is used.

In any case, I'd like to know how I can best move past this issue, workaround it, and install packages. Can I force an app to install, even if it's believed to be installed already? Can I attempt to do an "uninstall"? Any suggestions about this would be greatly appreciated.