It's a bit more complicated than that - when someone works under unjust conditions to make ends meet because of a law perceived to be unjust, the commitment towards respecting other laws is lessened.

As someone who has a wrongfully convicted, non-violent felon in the family, I can tell you it's easy to underestimate how difficult life becomes when you have a felony record. Landlords won't let you rent from them. Most employers won't hire you. Other employers will hire you, and then fire you later because the boss decided he wants to be tougher on crime. If suspected of anything else (or associated with anyone else suspected of anything), you are harassed by the cops in ways that I would have heretofore thought illegal (and that I since discovered are generally accepted, even though a lot of people personally thinks they're wrong). And this is when you go for the bottom-rung jobs, and the crappy apartments--forget about aspiring for more. All of this hardens and solidifies one's identity as a criminal--if you don't have a particular fortitude of character (many people claim they have this fortitude in spite of it not having been tested, and who knows, maybe certain ones do, but it is clear to me that most people don't), being treated in a particular way by society--especially a supremely negative way--makes you feel that way. When enough people treat you like scum, you feel like scum. Seeking out people who understand where you're coming from and won't judge you, you gravitate towards people with similar pasts. Seeking prosperity in a society that treats you as a second class (more like last-class) citizen, the opportunities in front of you range from dismal, cheap but legal to risky, remunerative but illegal.

So no--the minimum wage itself doesn't encourage crime--it's the treatment that comes with it. It's like the "college freshman poverty" meme, where college students talk about how poor they were because they can't afford anything but Ramen. While true in the literal sense (they don't have any money in the bank), it's patently false in a real sense--when they hold a minimum wage job, they're at the bottom of their almost inevitable rise towards middle class. When a convicted felon holds a minimum wage job, he's hanging on to it by a thread, simultaneously reminded of how lucky he is to be flipping burgers and how he's scum of the earth.

Now, stack this treatment up against the actual offense. You're walking down the street, carrying a few ounces of weed--you know, the stuff that pop stars openly discuss smoking, and that politicians now openly admit to smoking (in the past). You know you're being stupid--but hey, caution to the wind--maybe your father just died and you aren't caring much about your own future right now. Maybe you just lost your job and everything seems horrible. Maybe you're just another dumb young adult who thinks they're invincible. Regardless, you aren't hurting anyone. Heck, you're less dangerous than the timid but excited driver who guns his motor on the highway and breaks the speed limit after he's checked that there's no other cars in sight (after all, maybe he doesn't see the guy who's about to run across the street). You've known dozens and dozens of pot smokers and never seen one get arrested (the chances are quite small). You've smoked pot with dozens of people and never seen one overdose or have adverse affects. Regardless, you drew the short draw, and suddenly you're arrested and railroaded through a court system designed to efficiently process and incarcerate offenders--suddenly you realize that the arresting cop isn't Andy Griffith, ready to say, "Aww, Billy, I know you're a good kid, run along now and don't do it again."--instead there's a steady march of public defenders, prosecutors, judges, etc., who won't look you in the eye, whose main interest is in extracting a plea bargain so they don't have to waste time on a court date.

This is the narrative that goes through my mind when people prat about people making bad choices. There's bad choices (smoking pot, breaking the speed limit, creative tax deductions) and then there's BAD choices (rape, murder). So yes--society did something wrong--society KNOWS that people make bad choices in the first category (limited harm), and such choices are imminently forgivable, but due to a toxic mixture of lobbying, inertia, corruption, and ignorance, throws the book at those people, ignoring the torturous harm we're inflicting.