File sharing with ethernet shield?

I've searched a bit on google and haven't seen anything related to file sharing with Arduino so I'm not sure if it's even possible, but I'm not sure why it wouldn't be.

What I would like to do is pretty simple (in theory), I have an Arduino with an ethernet shield that I would like to plug into my local network, and from time to time I would like the Arduino to read a text file that is stored on a PC on the network.

Can this be done with Arduino or am I better off using a Pi?

Just about any web client example does that. That is what the internet is about. File sharing.

Here is mine in the playground.
http://playground.arduino.cc/Code/WebClient

// change this
    sprintf(pageAdd,"/",totalCount);
// to this
    strcpy(pageAdd,"/arduino.txt");

It is up to you what you do with the file after that. Parse it or save it to a SD.