That's most likely because 'Computer A' already has an account in the Domain already, while 'Computer B' would not. Your IT folks would take the form you submitted and create an account for 'Computer B' to join, then when you tried to join B to the Domain it would work.

Is your computer XP? (sorry if you mentioned it in an above post and I missed it)

-Zeke

My computers that I have joined using this process:
Countless Windows 2000 Workstation
Countless Windows XP Professional
SuSE Enterprise 8 via Samba 2.2
Mac OS X 10.3 via Samba 3.0

So whatever is going on behind the scenes, it is working for XP as well. This includes a base XP install off a normal CD, thus nothing weird in policy manager is being changed client side to allow them to join.