Wow. That's what people are up in arms about?
Rand clearly didn't understand where Rachel was coming from - and that's the key issue there. She wasn't trying to paint him as anything. He was unnecessarily defensive.
Rachel's point was that there are many people who do want private businesses to be able to do as they please. She was seeing the GOP becoming increasingly ready to question rights issues, and anticipated Rand's answer becoming very important in the future. She didn't try to accuse Rand of being racist or careless. She said clearly that she strongly disagrees with what seems to be his position - that any private operation should be able to do whatever it likes.
The only reasons that she didn't let it go were (1) that Rand wasn't giving a clear answer, and then (2) that when he did give an answer, he was acting as though the issue isn't relevant to today's politics or what might happen in the future if the issue was brought up for debate.
These videos are another example of Rachel's fair and sound approach to interviewing.
As for the recent video, she can't really be blamed for using the GOP figures rather than what Paul supporters want to be the case. She has to go by whatever the authoritative source says. Notice that she didn't say that people booed Josh Romney off stage, just that they were booing speakers' responses.
She's as fair as it gets with the information that she has.