I don't think he's lying at all on that one - but I get why you would think that. Giannis was born in a very poor Greece, and the environment where you spend your 0-18 years is the formative feeling that defines you.
From the way he talks at least, it's obvious that Giannis doesn't consider himself a true millionaire or "made" or whatever. It could be 10 figures in his bank and he'd still be trying to "secure his family's future" because there's just not a material price point to that feeling. Same way LeBron doesn't pay for Spotify Premium (which is the more idiotic thing to do tbh).
You nailed it about him having a childish outlook to some things though, and it's one reason I wouldn't like him on the Spurs. Seems like a very "you're either with me, or against me" type of dude, and that's a very annoying personality to deal with in any working environment.