Yes, there are sites that will not copy correctly even when using Ctrl-A.
Ran into this over the weekend at Wikipedia, even though everything in the browser is selected, only the text frame content is copied - the side and top frames don't make it to UR. I had to resort to Save As to .mht from within IE.
From Wikipedia:
http://en.wikipedia.org/wiki/The_Pri...ide_%28film%29
Yet other sites that use frames will be copied w/o problem. Granted there are a myriad ways to employ frames and various methods to achieve layout, but as a user it's difficult to know which sites are going to come thru w/o problems.