It seems that you are having some issues with the Slingbox video quality when you are at a remote location.
Basically, you are right. Although the Slingbox video quality is really good when at the local area network (LAN), you must meet certain requirements when at remote locations. The Slingbox need a specific connection speed when at remote locations; if the connection speed you get at the remote location does not meet the requirements, the video quality will be affected. The following links will provide you with the requirements for the Slingbox SOLO and Slingbox PRO-HD:
Finally, I recommend you to try to increase the connection speed when at remote location in order to take advantage of all the Slingbox features.
Hope this helps!