Crossing Wires

I am not a very good electrician.  I do, however, have a lot of experience running wires for various stereo components.  Which is why this particular problem really irks me that I can't come up with a better solution.

Here's the deal.  I have a HD digital cable box and a Tivo.  I love Tivo because I can record shows and keep them forever on my computer, something the cable companies will never allow you to do.  My point is to establish why I don't just get the cable company's HD DVR box. 

Anyways. 

The problem is with audio.  I run audio from the cable box to the TV and I can watch HDTV with sound, but I can't record any digital cable channels on the Tivo.  So I run the audio cables from the cable box to the Tivo.  Great, now I am watching HDTV in silence.  I wish like all hell that the second pair of audio out connectors on the cable box actually worked, but alas they do not.

My solution is rather backwards.  I ran audio cables from each of the sources on the TV (Tivo and cable box) to a 4 way AV splitter and then ran the OUT to the Tivo box with the cable's audio running into the Tivo.  In this case, the Tivo basically functions as a passthrough for the cable box's audio and the splitter lets me listen to either source while viewing it.

I still don't get exactly why it works though.  If the in's and out's on the splitter are labelled correctly then I shouldn't get any sound on either input, but I think they're "in" and "out" can be reversed as I did it.

Am I missing something?  Is there a better way?