Issues with connecting XBee to Arduino Uno R3
I am slightly surprised that you can actually talk to the XBee from your PC over USB with the XBee in the shield. XBee shields are generally designed for the XBee to be used by the Arduino only. The fact that you can actually talk to the XBee from the PC using X_CTU with the XBee in the Arduino shield, by holding down reset, seems to either be a quirk or a feature of the shield1.
Generally to use X-CTU to talk to the XBee, one would use an XBee explorer board or a Development board. One would configure the XBee completely in the Explorer dongle and then transfer the XBee to the shield for the Arduino to use it.
See the thread on the Digi forums, xbee s1 xctu arduino:

The shield is not design for writing and reading firmware to and from
the XBee module. It is only designed for basic two way communications.
If you want to read or write firmware to the module, you need to use a
board that is designed for it such as the XBIB boards from Digi.

See also Can an XBee be programmed with an XBee Shield.
However, hopefully someone with more knowledge of the internals of an Uno and XBee shield than I, could explain the actual electrical reasoning behind this issue. I have attempted to explain it below in the footnote.

1 Having said all of that, looking at some of my XBee shields, a couple have a microswitch, that enables the XBee to talk to either the Arduino or the USB, but not both at the same time. So, I guess that the need to hold the reset on your shield is because you do not have such a microswitch.
So the reason being, is that the Arduino and the USB can not talk to the XBee at the same time, as there would be conflict on the Rx and Tx serial lines - see this thread, UNO + Sparkfun's Xbee Shield Always Reset if Receiving Data From X-CTU Terminal which hints at the same thing. Two comments of note from that thread are:

It would be a lot simpler to debug the issue if you put the switch in the other position, and used SoftwareSerial to talk to the XBee and Serial to talk to the PC. Using one port to talk to two devices IS going to frustrate you no end.

and

Note that a communication application connected to an arduino that opens a com port, sends data, then closes may cause the arduino to reset.

As a (really wild) guess, I would imagine that the USB-to-TTL IC's DTR line, or equivalent (?), is [logically] tied to the Arduino's RST line, so that if the PC tries to communicate to the XBee, it ends up resetting it, rather than signalling to the XBee that it is ready to communicate.
Note: The USB-to-TTL IC could be a FTDI, ATmega 4U2/8U2/16U2 or an FTDI clone, depending on the variety of Uno that you possess.
Addendum
I do wonder why the switch is there, if it doesn't end up working correctly. Regardless, I would still get a $3 explorer board clone to use with X-CTU. Be careful which one you buy as not all of them work with OS X, if you use a Mac, see the end of USB-TTL interface devices on OS X. That explorer,  XBee USB Adapter Bluetooth Bee FT232RL USB to Serial Port Module for PC Arduino, is good value for money and compatible with WinTel, LinTel and OS X machines: