It depends on where you're at in residency. If you're an intern (which is what the CNN article talkt about), you're not likely to get any sleep, especially surgical interns. The higher you go in residency (i.e. seniors) will only get up when needed or after the work has been done by the intern.
The hospitals do provide beds, but most of the time, there is way too much work that has to be done, pages that have to be returned, lines to be placed, H&P to do,...... Then you still have to write your daily notes on the patients that you normally round on. If you get sleep, its only 1-2 hours.
I wonder if any more changes will happen eventually. I did'nt know the EU had such strict restrctions on work hours. It'll take years before any more restrictions take place in the US, because a lot of attendings I talk to say the we already have it WAY easier than they did. A maximum 13 hour shift seems unimaginable.