From my understanding there will be a single one-off UAC popup which will allow a service to be installed with higher rights - that service will then carry out installations from that point on, and will be able to do so silently, as it will have the rights to do so.
Chrome avoids it by installing into the User's own folder. Firefox is installed in Program Files, which requires user authorisation.
Arguably, this is the correct place to install, as it means that the application is usable by anyone on the PC, rather than having to be installed for each user individually.
Chrome does a non-standard install and also can be self modified which isn't secure. Chrome could be replaced by a keylogger+chrome by anything running on the system.
That's why admin privileges are required for accessing Program Files to begin with.
Using a separate updater process is actually the clean way to go, on Windows.
