Does CS6 upgrade licence require CS5 to remain on the machine?

you don't need cs5 to be installed even when installing and activating that cs6 upgrade version.

to activate your cs6, you just the serial number of cs6 and cs5. when starting the cs6 installation, you will be prompted for your cs6 serial number.  the installer will check and find that's an upgrade serial number and then it will search your computer for an activate cs5.  failing to find that, you will be prompted for that cs5 serial number.

enter the correct number at the correct time and installation and activation will proceed.

bottomline: if cs5 is installed, you can uninstall it but secure both cs5 and cs6 serial numbers before uninstalling.

p.s. have you recently activated your cs6 (so it's no longer on the 30 day trial)?

No, it does not... and unless you have an install problem all you need is your CS5 serial number when installing your CS6 upgrade version