It seems like the issue comes down to the sequence of installing updates, both to the existing installation, and to the setup program. The specific scenario was:
- The initial install of SQL Server had been done directly from the slipstreamed SQL Server 2012 service pack 1 setup. At this time, the server was not connected to the internet, so no additional updates were applied either to the installed components, or the setup program
- When attempting to add the Full-text service, the server was connected to the internet, and had the option set to install updates to other products via Microsoft Update. When I started the setup (which used exactly the same initial source), the setup downloaded an updated setup, and also found a 145 MB update rollup that would also be installed
- Part way through the setup steps, setup failed with the message "Registry properties are not valid under this context"
The solution was to go to Microsoft Update and install the SQL Update Rollup, then go back and run SQL Setup to add the extra component. Interestingly, SQL Setup still reported that it had found this 145 MB rollup to apply, even though it was already installed