Rutherford's daughter Ella, 13, was also riding with her at the time, but was not hit.
Rutherford has been in hospital since the Dairy Flat incident on August 21.
"I'm not sure where to start," she said in the Facebook video.
"How do you thank people who have just been so generous with their thoughts and wishes in the last eight days, I'm just so grateful, as is my beautiful family, for all the love and support you've shown us," she says in the video.
"My leg has been degloved. I won't be wearing a miniskirt for a very long time. 'Woohoo', I hear you say! It's not pretty, but I have a leg, and you've got to be thankful for that.
"I went flying through the air and I hit that windscreen with an almighty force. But when I opened my eyes in that ditch, I just thought 'wow, I'm alive. This is cool, I'm okay'. Then the panic set in."
Prime Minister John Key has ruled out making tourists pass a driving test, as it would mean "retaliatory" action against Kiwis driving overseas.
"I don't think the answer would be running people through a very short-term test I don't think that is likely to work."
He said a testing regime would be likely to be replicated overseas.
"I think New Zealanders when they went overseas and had to get tested they would find that very frustrating."
He said the rate of tourist-caused accidents was "certainly not perfect but it has improved".
He spoke of other initiatives such as tourism operators, rental car companies educating tourist drivers, arrows painted of the right hand side of the road, and educational videos on Air New Zealand planes.
A foreigner that holds a valid overseas licence in English and that hasn't been disqualified is allowed to drive in New Zealand if they have been in the country for less than a year.
Official figures from the Ministry of Transport show foreign drivers caused 19 deaths last year, 113 serious injuries and 616 minor injuries, Mediaworks said.
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