I am answering my own question.
It turns out that my Camry has a diversity antenna and an antenna
booster.  The Crutchfield guys (they are great) figured that out and
suggested that I check if I wired up the blue wire from the Pioneer
head unit to the blue/white wire in the harness supplied by them and
after I fixed that problem everything works.

So, I have the bigger antenna connector going into the Pioneer HD
tuner GX-P10HD unit.  The output of the HD tuner is fed to the main
headunit using Pioneer's own IP-Bus cable which comes with the HD
tuner.  I now have the blue wire connected to the blue/white wire.
(BTW, any time someone mentions colored wires, don't you want to
scream: "Don't cut the red wire!  Cut the blue wire!!! Kaboom!!!!")

The whole system from Crutchfield along with their support was so nice
that people think that the mounting is part of the factory install!!!
I had thought about buying from some other store for less money but
Crutchfield included the right mounting, correct harness, and
wonderful after sales support.  They kept at it till my problem got
resolved.  Actual dollar difference was max $20 after adding the costs
of all the parts.  On the other hand, I got support worth few hundred
dollars and the right look.  To my good-looking half, the look is very
important!

The Pioneer DEH-P7000 BT comes with BT handsfree profile and a zillion
other profiles including bluetooth audio streaming.  After pairing,
the address book gets copied over to the Pioneer from my Blackberry
Curve (8320).  Calling and answering calls is easy.

The best part is that you can play your music loud and an incoming
call will cut off the music and ring the phone.  BT connection is
easy:  you just walk into the car and it connects with the paired
phone.

No echo, clean operation.  Sony sucks.

Many add-on BT units have issues that require you to connect
explicitly every time you enter the car.

The controls takes some getting used to and very hard to operate while
driving.

Another short-coming:  addresses max out at 400 per addressbook.
There are 3 address books, one per paired phone, three paired phones
max.
USB, iPod, extra is great.  Just attach a simple USB drive and listen
to music.

HD-Radio:  Clean cutover from analog to digital when signal is good.
In the bay area I can finally listen to KDFC HD1 and HD2 (102.1) with
no noise.