Hmmm. This one's a bit thorny.

The "Arduous March" (북한기근) skirts /r/AskHistorians' rules concerning 20-year content, as it technically occurred between 1994 and 1998, but in truth, the set of circumstances that created the famine predate it by several years. Historians argue that the policies that contributed to it actually predate the famine by several decades, and the system that dictated how North Koreans responded to the famine had been in place just as long, so I hope the mods are okay with a little date-fudging.

Did government oppression in North Korea get worse during the famine? It did and it didn't. I realize that's a magnificently unhelpful and simplistic answer, so let's try to expand on it a bit.

Disasters are a major crisis of legitimacy for government. One of the reasons that organized human societies exist in the first place is to prevent, or at least ameliorate, the kind of problems that threaten to wipe out that society, and famine is one of the big ones. If Amartya Sen is to be believed, it's also one of the most avoidable. Left to their own devices, humans are pretty good at finding, raising, growing, and storing food. They're also pretty good at keeping track of those efforts: Some of the earliest records of organized societies that we still possess today, the clay tokens from Mesopotamian cultures c. 8,000-7,000 BCE, concern crop and livestock counts.

When a famine hits, the government has failed at one of its most basic functions. As a result, citizens generally don't have much confidence that it's any better at more advanced responsibilities, or even deserves to exist at all. For a government like North Korea's, whose legitimacy is derived from its creation at the hands of a national hero, Kim il-Sung, and its passage to his heir, Kim Jong-il, that's a huge problem. Politics and culture were, and remain, so thoroughly intertwined in North Korean life that no criticism could possibly be leveled at the state without implicitly criticizing the Kims.

So. The North Korean government has been and remains extremely sensitive to its portrayal both domestically and within international discourse. Domestic criticism was an oblique criticism of Kim il-Sung and Kim Jong-il, which could never be tolerated: International criticism was seen as part of the world's hostility to the North Korean regime and its class of elites, and could never be allowed to reach the North Korean people themselves as -- again -- it would be seen as criticism of the Kims.

Why 1994 was a particularly bad (but perhaps inevitable) year for it all to come crashing down: To give a bit of context as to why the North Koreans were especially sensitive to both domestic and international opinion in this period, we should consider that:

• One of its major supporters, the Soviet Union, no longer existed as of the late 1980s. That wasn't a good thing for NK's perception of both internal and external security, but the problems ran much deeper than that. The end of the Soviet "friendship prices" program, which had allowed North Korea to buy things like oil and fertilizer at 25% of their actual cost, is the major shock that probably precipitated the famine, although it didn't really cause it. The Russians had their own problems at the time and refused to bankroll NK's economy, which had never really existed as anything other than a dependent of its Soviet counterpart. The Russians were also well aware of NK's propensity for never repaying loans or honoring barter agreements. You want oil, tovarischch? Cash up front, please.
• It has watched its rival, South Korea, throw a very successful Olympics in 1988. The role of the 1988 Olympics in North Korea's downward spiral is a pretty interesting thing to study, but that's a discussion for a different day. For our purposes here, let's just say that NK wasn't able to convince most of its allies (or "allies") to boycott the 1988 Olympics on its behalf. It also failed in its bid to get the IOC to allow it to co-host events with South Korea, probably because the IOC is 5% less stupid than it looks.
• It had since watched South Korea court many of NK's traditional friends with valuable trade agreements. The most visible among these was China, which established formal relations with South Korea's government in 1992 over NK's strenuous protests. For the Kims, that was a massive and irrecoverable loss of face, and that was on top of the disquieting knowledge that China didn't value its relationship with NK over the opportunities that a relationship with SK would give it.
• Kim il-Sung died in 1994. Kim il-Sung was the founder of North Korea and greatest hero of the Korean people -- again, as the North Korean state saw it (historians see it a little differently!). There is a portion of me that wishes he had lived to see the end of the famine, because in all truth, he is almost certainly the person with the greatest share of responsibility for the fact that it happened at all.
• The system had already begun to fail. One of the reasons that historians and statisticians think that North Koreans hadn't been getting enough to eat for a long time is that the army started dropping its height requirement for incoming recruits in 1991. That was for young men who'd been born 1974-1975. Rations through the Public Distribution System (PDS) also declined precipitously after the Soviet Union fell. The system just kind of stagnated from the mid-1970s onwards (which is actually quite a close match to outsider estimates of North Korea's GDP), and then started a dangerous free-fall in the late 1980s.

What does all of this have to do with government oppression during the famine? It explains much of the government's motivation during the early part of the famine. They couldn't fix the underlying cause without admitting that the Kim regime's policies (and thus Kim il-Sung himself) were ultimately at fault, so they tried to criminalize many of the public's more obvious coping mechanisms. However, their ability to do this was itself negatively affected by the famine and breakdown in public order, and some of the more traditional punishments (e.g., execution or family imprisonment for defectors who got caught) faltered as authorities realized that that would mean slaughtering or imprisoning mass numbers of people.

So yes, what we would see as "government oppression" increased during the famine in a sense. The government shut down private markets, harassed farmers to keep them on government-owned fields as much as possible, jailed and/or killed people who stole food, punished people who traveled without permission, and jailed/sometimes executed defectors who'd been caught. Punishments varied by local circumstances, the social class of the offender, and whether his/her family could afford to buy off the officials involved. (More on bribery in a bit.)

No, government oppression was not worse in the sense that the same government system that produced the famine also broke down significantly during it. Whenever a government makes rules, someone has to enforce them, and if that somebody is more worried about finding food for him/herself than doing their jobs, well ... don't count on those laws remaining sacrosanct. Corruption became an entrenched and pervasive element in North Korean society, as people bribed guards and bureaucrats to look the other way while they traveled and bought, bartered, or stole food. Which, as Haggard and Noland pointed out in their statistical study of the famine, had its own sad effect: North Korean society was divided between the people who could afford to pay these bribes, and those who couldn't.

To borrow an example from Nothing to Envy, which would be a great book to pick up on matters related to your question:

One day as the women were picking corn (in the prison camp for defectors), the camp director came to deliver an impromptu lecture in the cornfield. It was the usual fodder. He urged them to arm themselves with the ideology of Kim Il-sung against the temptations of capitalism and to commit themselves to their nation.

Then he asked for a show of hands: Who would promise not to run away again to China? The women squatted in sullen silence. Oak-hee looked around. Not a single woman raised a hand.

After an uncomfortable silence, the prison director spoke up. “Well, if you go to China again, next time don’t get caught.”

Such was the might and power of the totalitarian North Korean state in the late 1990s after years of hunger. This is what historians mean when they say that major disasters are a crisis of legitimacy for government.

TL:DR: The government attempted to criminalize some of the more embarrassing outward signs that the famine was happening, but if you're expecting people who are themselves hungry and desperate to enforce unproductive laws, you're gonna have a bad time.