If there's any doubt left in her mind on whether or not Kai would have done that, Shinji would be happy to confirm that, yes. That's exactly what would have happened.

"If there's a plan, it's my first time hearing about it." It's all probably just jokey banter, he's sure, so there's no real offense is being taken here, even if he punctuates the thought with a tiny puff of a sigh. "Not my fault it never got this cold while I was growing up."