"It's a distribution problem", which is to say "It's a capitalism problem".
This is exactly right. World hunger today is an emergent consequence of the global capitalist economy. People who were once able to grow crops to feed their families now have their land aggressively taken over by corporations (often with threats of violence). They then have no choice but to work growing whatever luxury crops the corporation dictates, such as hot peppers or coffee - crops that are rarely capable of sustaining a community. Then, whenever the value of that crop plummets or there is a drought, these communities are left without money to buy food.
Even during the worst famines, marketplaces can be seen selling an abundance of food. Those that die of hunger die not because there isn't food available. They die because they cannot afford it.