If you installed it via an .MSI (like the linked questions seems to indicate they did) then technically you didn't install it, the Windows Installer Service did, which runs was the "LocalSystem" account which has permissions to write to places your user account can't.
From MS, about using the LocalSystem account for service log ons:
It (the LocalSystem account) has extensive privileges on the local computer, and acts as the computer on the network. Its token includes the NT AUTHORITY\SYSTEM and BUILTIN\Administrators SIDs; these accounts have access to most system objects.
If you lunch an MSI under an 'Adminsitrator' account it will prompt you if it needs to make any system changes, unless you have UAC turned off, then it will just do it.
The VirtualBox .EXE installer is a wrapper for an MSI. When you get about 2/3rds of the way through the setup wizard it stops and asks if you want to allow the now-unpacked MSI to write to the system (in VirtBox's case, to the public desktop, and to the system network settings, at least).
If launched as a standard user, the installer stops at that point and requests Administrator credentials to continue.
So if you managed to install it, you did it with Admin privledges, you may just not have been warned (UAC is off) or you just don't remember allowing it when it prompted. :)