Everyone (maybe not Jenn) was after Frank, everyone was basically lying to him. There was literally no way for him to turn where he wasn't going to be targeted. He saw a guy with his back to the wall willing to work for him, being completely honest and took a chance. Now, did he make a mistake?
An hour or so ago, on the feeds when they were alone Dan said to Dani, we have to get rid of Frank once and for all. Interpret that as you will. But seems to me that Dan don't think its against their deal if Frankie goes up and out during Ian's HOH
Edit: In effect, what really happened was Dan/Dani supplanted the initial Brit/Shane side deal with Frank that they did before the HOH comp. So Frank was taking a crap deal either way, it just seemed more sincere coming from Dan. But because he went with it he took the chance of keeping the stronger player around.