Using Arduino and XBee at the same time I have 2 Arduino Unos, 2 XBees and 2 Wireless Proto Shields. The first setup has a humidity/temperature sensor (SHT21P) and it writes data to serial and it works (I've tested it).

Now, the other Arduino with shield and XBee is plugged in my PC to get data from the sensor. So here's the problem: as far as I understand, I can't use XBee and Arduino at the same time, because USB and Arduino both use TX/RX pins to communicate to PC/XBee. I've tested both of the XBees when they are powered with DC jack and they both work. So can anyone confirm that it's true that they're not made for being used by PC and Arduino at the same time? If so, how can I get the data to my computer?
If I understand correctly your goal is to receive data on your computer from an arduino connected with xbee? You could use a USB > Xbee board similar to Sparkfun's Xbee USB explorer board. I am not familiar with the shield that you are using, but some xbee shields allow you to select the pins that the xbee is connected to. It sounds like yours is defaulting to Pin 0 and Pin 1, hardware serial on the Uno. If you can switch it to Pin 2 and Pin 3 (or any two digital pins) you could use software serial with the xbee, leaving hardware serial free for your USB connection.