The whining that you hear is from the LPFP. I had the same problem and my dealer replaced mine about six months into ownership. It was a high pitched whining sound that seem to be coming from behind my seat. Anyway after the dealer replaced the pump two years ago, I have never had a problem with it.
I have a 35i which has the HPFP. I never experienced any problems with that, but my dealer replaced it anyway as it was a recall. The people that had problems with that had the car going into a limp mode, there wasn't any sound coming from that. The whining sound is from the LPFP. I would take it to another dealer as your dealer apparently doesn't have a clue.
2010 Z4 35i - Orion Silver, Ivory white extended leather, anthracite trim, premium pkg, sport pkg, premium sound pkg, cold weather pkg, navigation, 6 sp manual
2006 Z4 30i - Monaco Blue, beige leather
2003 Z4 2.5- Sterling Gray, black leather
1998 Z3 2.8 - Bright Red, black leather