I have a similar background, but I can't say I adapt my language to that of upper classes. My accent and skin color pretty much gives away my background when I utter my first word, and unfortunately, just like having a southern US accent, people are subconsciously biased to thinking I'm probably not too smart. I love using "ten-dollar words"[1] - not that I shoe-horn them in, but they are the ones that usually pop into my head first and I can't be bothered to water them down. Additionally, I figure, "dumb" accent + "smart" words cancel each other out - more or less - which puts me on equal footing with my "normal" sounding colleagues. It's easier to change/adapt my vocabulary than it is to change my accent.
I love language, I do a lot of reading, and it's a delight when you find the right word that precisely expresses what you're thinking. Reading a lot expands your vocabulary and improves your adeptness at deploying it. When done in moderation, using puns and subtle literary references is fun (even when no one picks up on it) - as long as it doesn't detract from the actual message I'm communicating.
1. I do not mean speaking like the Architect from The Matrix here. The other week, I was called out by a monolingual collegue for using "nomenclature" rather than "naming convention" or "naming system" - which feel kludgey to me. Also, when I do make the effort to use shorter words after thinking of a long one first, that adds brief pauses to my speech, which gives the appearance of an ineffective communicator.
And, of course, there's the style of clothing, haircut, makeup, accessories, etc. Pretty much everything :-)
If you talk about holidaying with one's family in some exotic locale or of having a summer home in the Hamptons, the person you're speaking with can surmise that you're not poor.
The rich kids in that documentary also regularly go out to bars and think nothing of spending hundreds or even thousands of dollars on champagne.
It's definitely not just about how one talks that signals to others that one is part of the upper class.. but once one is established as in the upper class, then things such as one's manner of speech might distinguish you.
So the scenario in question is "someone trying to fit in with the upper classes" to which your response is something like "use the language however you like"--which is a fine thing to say, and no doubt especially easy to say for those of us who have the ability to speak in the upper class dialect/register, but that's not the stated goal. I.e., if you're trying to fit in with the upper classes, using "utilize" is a tell that you don't fit in (IMO the upper class register prefers to use very few words to convey a lot of meaning; precise, terse, and fashionable vocabulary is the name of the game)--if your goal is to use English however you like, and if you like "utilize" instead of "use", then go right ahead.