This is true for
properly written installers and apps, but since not everything is properly written, a related problem does crop up from time to time: an installer or app assumes the user has permissions to something that the "admin" group usually has access to, and therefore doesn't bother using the correct API to elevate. Even here, though, in the typical cases of installers and updaters, there are easy workarounds that at least don't require logging out or giving additional rights to the logged-in user: fast user switch or login(1) to an admin user, then retry from there.
The only thing Windows does differently here is that it provides a silent, non-admin workaround (filesystem and registry virtualization) for buggy applications, which works, but which can be problematic in other ways. Most notably, while OS-level workarounds are a clear win for older and otherwise unsupported software, they reduce motivation for developers to fix bugs in current software papered over by Windows' workarounds.