And none of those remotes that I have mentioned are paired to anything.
all of the remotes you mentioned use IR and have no need to pair.
There is a pairing option for the IR remotes, but it's a "dumb" paring, The remote has no knowledge of the existance of the receiver.
With the IR remotes, There are 256 different sets of all the commands, so for example "Play 120" or "Play 100" and "Up 120" or "Up 100"
When a receiver is paired, it ignores the commands that don't match the correct number.
When a receiver is unpaired, it will listen to any command, irregardless of the number.
Most third party remotes like the harmony, choose one code and are stuck with that.
The apple remotes will randomly change to a new code, I believe it happens when you use the pairing button combo on the remote.
There used to be (i'm sure still around somewhere) a harmony profile that mapped every button on the remote to a different combo ("1" was "play 50" -- "2" was "left 50" and so on) , and with the right software on an older mac with an IR receiver, you could use all the buttons and map to different software.
Was very handy back in the day with Plex/XBMC running on a mac.
(I'm not sure if this even still applies to the various versions of the aTV4.)