Windows 7 can't install from Kingston USB stick

I recently discovered that it's impossible to install Windows 7 from a Kingston USB stick. It turns out this is a known problem with Kingston DataTravel sticks. I had this problem while installing Windows 7 Pro on an old Panasonic Toughbook CF-31.

It's not obvious that you can't install from these USB sticks, since you can boot into the Windows 7 installer. Everything works up until you're partitioning your harddrive. There, you'll get an error message saying:

Setup was unable to create a new system partition or locate an existing system partition. For more information, see the Setup log files.

Screen shot showing the error message while installing Windows 7 from a Kingston DataTraveler USB stick.

Solution?

Use a different USB stick. I had a SanDisk stick that worked as expected.