What exactly are the rollbacks in Higurashi?
I think the correct answer lies between what you're saying and what Wiki is saying.

Here's a definition of "kakera" (usually translated as "fragments") from Umineko no Naku Koro ni (the installment of WTC after Higurashi) EP4's TIPS:


  Worlds of different fates and circumstances are called kakera, and
  witches who are able to cross the ocean of endless kakera are called
  Voyagers.


Hanyuu is taking Rika through different kakera, but she is also going back in time. If she just went to the same time in a different kakera, it might be too late for Rika to do anything. I believe towards the end of Higurashi, Hanyuu also states that her power is weakening and she can't go as far back in time.

If you're interested in knowing why/how Hanyuu has these powers, I'd definitely recommend playing the Umineko no Naku Koro ni sound novels or maybe even reading the manga. Don't watch the anime though... It doesn't cover that far into the story.