You are half right. Most large companies do indeed build their own servers, because that way they can get exactly what they want.
Granted, all the parts come from big name suppliers and they don't tend to fiddle with lots and lots of different parts, but they do tend to buy something like this:
One mostly bare Dell Powerdedge server from Dell
4 GB RAM from Crucial
Two 120GB drives from DrivesDirect.
Two network cards from Intel.
The box arrives, the hard drive is pulled out and discarded, the new drives, RAM and NICs are installed, and an OS is installed.
Then it goes into the rack. One NIC is used for normal network communication, one NIC is used for the management network and one is kept for a hot spare.
I've built file servers, print servers, firewalls, LDAP servers, Kerberos servers and various specialty boxes in just this method while working for more than one Fortune 500 company and half a dozen Fortune 1000 companies.
Companies without an IT department generally take what Dell or HP gives them. Those companies are generally a lot smaller and buy complete support contracts for software and hardware.