Actually, what you were told is accurate, with the exception of Podtrapper.
Basically, to listen to music etc via the built in BB Media player you need a headset with A2DT stereo support. One of the reasons I picked up the Jabra BT-8040 is that even though it is a tiny one ear headset, it is one of the very few that supports A2DP and will accept a stereo stream (not very useful for music but great for voice content like podcast and audio books). Unfortunately the noise reduction on the BT-8040 does not compare to my Jawbone so I kept both.
I specifically bought the BT-8040 to use for voice content via A2DP but the lack of "bookmarks" in the built in BB Media player led me to discover Podtrapper. I immediately noticed that with my Curve 8300 the BT-8040 would work on both the "Bluetooth" and "Stereo Bluetooth" Output settings on Podtrapper. I then tried my Jawbone (which never worked with the built in BB Media Player) and found that Podtrapper would stream to it fine on the "Bluetooth" Output setting.
There are two BT profiles involved here: "Headset" (typical mono) and "Stereo Headset" (A2DP Stereo)
Not sure how, but Marcus seemed to have found a way to get Podtrapper to stream to headsets that are paired in the "Headset" profile, but as I indicated in my original post it seems to vary depending on the handset involved - works on my 8300, not on the 8330 with the same hedsets.
So, at least at the moment on our 8330s you need a BT device that supports the A2DP "Stereo Headset" profile.