Their "DIY Edition" (vs "Pre-built") allows this: the laptop comes without memory and storage installed, and you either install your own or install separately packaged parts that you ordered at the same time during the configuration process.
I think it's fine to require that you cannot use work equipment for personal projects, but claiming ownership of a project written on the weekend on a company laptop isn't the solution.
For some reason instead of redirecting you to login kagi.com/assistant redirects you to the wiki rather than a login page when you're not logged in.