The problem is that people have adopted the term rooted to also mean access to the root of the filesystems, iow, the / directory. ("Just place this file on the root of your SD card," being the most common example of that usage.)
Anyway, with / access you can remount /system to rw instead of ro, and from there you can install the su binary (either in /system/bin or /system/xbin depending on how the dev made the installer).
The apk is simply the front end (user facing) management layer.
And then toss in the common Linux misunderstanding that's bled over to Android that su stands for super user. It doesn't, it stands for set user, but without arguments (the way most people have seen it) defaults to setting you to the root user.
As a Linux user, it might be just as well to think of the apk as your sudo access assistant, and to think of the grant/deny popup as analogous to confirming access with your password.
If you haven't already, install a good busybox (I prefer this one) -
Check out "BusyBox"
And then Terminal Emulator and look around just as you would on Linux.
Your filesystem layout will make more sense one you use the df and mount commands there.
Hope this helps.
PS - Also, a thank you for taking down the pro download.
Thanks for the good info... so the apk's are often about getting the bin/xbin files to /system and having a management ui for it
what methods are employed to get the initial root access though? aka "rooting the device"