The "Fox borrowed the might of a tiger" is a Chinese saying (I'm not sure if it's also a saying in Japan). If I remember correctly, the story goes: a tiger captured a fox and was about to eat him, when the fox told the tiger, in a haughty manner, that he is actually the king among animals. The tiger didn't believe him, so the fox asked the tiger to walk behind him and observe how all the other animals run away at the sight of the fox. The tiger agreed and saw, indeed, all the animals fled upon seeing the fox. What the tiger didn't know, was that all the animals fled upon seeing him. It means someone weak borrowing the strengths of a strong person for their own advantages.
Here it's changed to racoon dog (aka Tanuki) because that's Nozomi's "spirit animal". XD