It does when you have more than 1 browser tab that has a video present on it (i.e. YouTube), and you have initiated play-back on both videos, even if the video in the "background" is paused or stopped. The longer I leave a video that has been "initiated" in a background window open, the worse the stutter gets until I have to restart Safari.
This, btw, is without flash installed.
I would attribute it to a memory leak of some sort, and if you're saying that this doesn't happen to you, then perhaps my hardware is damaged somehow (although I've brought my computer into the store multiple times, and they've done full OS reinstalls and hardware scans to no avail).
Basically, the 1st gen Macbook is suitable for some casual users, but not all. I just ordered an m7 refreshed version that I hope won't suffer from this issue. If it still happens, then it just means I'll have to move back to a Macbook Air until they come out with some hardware that can support the way I browse the internet (i.e. having 5-6 tabs open simultaneously).
If you only use your browser one window at a time, without tabs, I doubt you'd encounter video stuttering.