I think the answer depends on what you mean by your question, which you stated as:
Is it "a known risk that people are dying of starvation because we cannot produce enough food"?
As is often the case, we'll need to go into what some of those terms mean. To start with, the risk part you quote is certainly an unlucky choice; if people are dying of starvation, it's not a risk, but a tragedy. Let's start by changing the question to Are people dying of starvation because we cannot produce enough food?
Now, this can have two meanings:
- Is enough food being produced worldwide for everyone to have enough to stay alive?
The answer to this one seems to be yes. Although I could not find the original FAO statement, most reputable sources (e.g. the WPF, Oxfam and others) agree that there would be enough to go around (although, once again, I have not found a publication with a clear source indication for this statement).
- Would producing more food mean less starvation?
The answer to this one is also yes. The FAO, among many others, has clear recommendations which include a significant growth of agricultural production to ward off famines and starvation now and in the future.
In fact, you can more easily see the (false) dichotomy when you imagine two extreme scenarios. In the first, the world produces exactly as much food as is needed for everyone to have just enough to eat. You could say that any occurring starvation would be only a result of mismanagement; however, it is obvious that an absolutely perfect distribution is impossible - if one egg is dropped somewhere in the world, someone goes hungry. On the other hand, if every town and village produces a hundred times as much food as it needs, there is hardly any chance for even the grossest mismanagement or inequality to produce hunger.
To sum up: the worldwide food situation is influenced by many factors, and both production and distribution are among them (in fact, the FAO report cited above has six groups of security indicators: availability, physical access, economic access, utilization, vulnerability, and shocks). It is an almost undisputed consensus view that we could significantly reduce or even eliminate malnutrition by, among other measures, redistributing the existing supplies. However, it is equally clear that we could reach the same goals by increasing food production. Which of these is the better way is a matter of dispute, with most organizations (such as the UNICEF, Oxfam or FAO) suggesting a combined approach.