This has been brought up before. It turns out that they claim it did originate in the house since the Senate took a bill that came from the house and wiped out the text and replaced it with Obamacare. Now obviously this is a form of Fraud in a sense as it is subverting the intention of the constitution, and the founders. But I guess it is not the first time it has been done.
Here is some info on how they used a house bill.
http://www.freerepublic.com/focus/f-news/2901226/posts?page=6#6
"They claim" is the key phrase here. They claim all kinds of things that are lies. If the SC has a shred of decency left they won't let them get away with blatant fraud.