Still not sure you have all the facts here. The question to K was "did you speak to anyone at X, X & X, the law firm that is Trump's personal lawyer, about Mueller?"

It's not inappropriate for POTUS to himself speak to someone he's considering for the job, or to have the WH counsel and/or WH staff interview that person. Nothing at all wrong with that.

What's inappropriate is to have his PERSONAL lawyer speak to Kavanaugh. K is potentially being hired to work for the USA, not for Trump. Now, why in the great big world would his PERSONAL lawyer talk to K about Mueller? Does that not look a tad suspicious to you?

Now, lets say K never spoke to those guys about Trump and Mueller and she's just trying to trick him. All he had to do was say 'fuck no' to her question and move on. The fact he's trying to dodge the question is suspicious.