We are above something if were are too moral to do it:
He was above denying his colleagues' share in the credit.
If we are too wealthy to deem to do it:
He was above worrying about where his next meal will come from.
Or if it will make us look bad, or we are of too high a social standing:
I am above getting into petty scraps in public.
In contrast therefore, we are not above something if we are not too moral to do it:
Jeffrey Archer is not above sleeping with prostitutes, bribing them, and then perjuring himself in false libel actions.
If we don't care about something making us look bad:
Jeffrey Archer is not above claiming to be the youngest ever MP even though someone seven years younger was already sitting in the very same parliament.
Or if we have the money to avoid doing something odious:
Jeffrey Archer is not above writing trashy novels that treat the English language worse than he does prostitutes, journalists, and the truth.
Generally, when we are above doing something, it means that we don't do it because we are "better" than the sort of person who would, for some value of "better" (wealth, morality, wisdom, privilege, social standing, esteem, self-esteem). When we are not above doing something, it means that we do do it, because we are "worse" than the the sort of person who wouldn't, likewise by various different criteria.
In most cases, to say someone is above something means that they didn't do it, and we approve their not doing it, while to say that they aren't above it means that they did it and we disapprove. So, in my examples about Jeffrey Archer, I'm saying that I disapprove of his behaviour in each case. (Since you'd mentioned him, and I needed examples of odious behaviour, they came quickly to mind).
Pause before I move onto the exception. Don't read the next bit until you're happy you understand the previous...
Okay, the exception is when the "better/worse" relates to privilege. Here we if we say that a rich man "isn't above working with his hands" or a boss "isn't above helping out on the floor when it's busy" we mean that they aren't using their privilege to shirk such work, and we probably approve of that.
We might also use this "above" idiom in a sarcastic way, so saying "oh, he's above talking to the likes of us" could mean "he thinks he's better than us, but really he isn't". But this is a sarcastic use of irony, so it's a deliberate inversion of the normal meaning.
In the example given, the speaker doesn't approve of the fact that William Kane talked to the lawyer whether because he thinks it sneaky, thinks it bad form that he is engaging a lawyer outside of the family firm, thinks it bad form to enquire so closely after finances (an attitude among very "old money") or some other reason (or no sane reason whatsoever and it was just badly written).