Audio out: 1st Gen vs 2nd Gen

I've read all about the problems with 3rd party AV cables, and this is not another one of those posts. I have a 1st Gen Touch with firmware 3.1.2. I also have this dock: http://bit.ly/99XCp7 Basically, it seems that the dock just extends the 30-pin out. There are 2 ways to send the signal from the dock to my tuner: 1) aux/stereo plug-to-RCA jacks or 2) 30-pin-to-RCA jacks (like this: http://bit.ly/7Qhe4W). This setup works fine for playing tunes from my 1G Touch.

My son has a 3rd. Gen Touch, also with firmware 3.1.2. When he uses the dock, the charging function works fine, but he cannot send any audio out. This is a pain. My guess is that this is a similar problem to the AV cable issue.

Question: If this is a firmware issue, why does my Touch work with this dock when it has the same 3.x firmware?

Question: If I downgrade the 3rd Gen's firmware to 2.x, will that resolve the cable issue or is the problem also in the hardware?

Any help is appreciated.