The null hypothesis (people with symptomatic covid are as likely to get severe symptoms, regardless of whether they received the vaccine) predicts this many cases with severe symptoms:
30 / 185 * 11 = 1.7
1.7 ~= 0, so the sample size is too small to support the headline.
If you take a Beta(1,1) distribution as your prior, then the control group's risk-of-severe-covid-given-symptoms posterior is Beta(31,156), and the experimental group's conditional risk posterior is Beta(1,12).
Drawing 100,000 samples from these distributions (`betarnd` function in matlab) gives an 87.8% sampled likelihood that the intervention reduces the conditional risk (intervention(i) < control(i)), and a 64% sampled likelihood that it reduces the risk by at least half (intervention(i) < control(i) / 2).
This is suggestive (but not yet "clearly convincing") evidence that the vaccine reduces the risk of severe covid conditional on being infected in the first place, and that comes on top of the obviously compelling evidence that the vaccine reduces the baseline risk of infection.
This conclusion makes intuitive sense since the vaccine is intended to produce an immune response. A patient who has a moderate response to the vaccine itself may not neutralize the infection before developing symptoms but would still have a primed immune system to control the disease before it becomes severe. (That is: the response to the vaccine intuitively falls on a range, rather than being "all or nothing").
I find an interesting related item to be the ~30% of people in the AZD1222 (AstraZeneca) study who got COVID after being vaccinated. They reported that in this subgroup, there were no severe infections, nor any hospital visits, confirming the parent's hypothesis that some people might not get full immunity, but still benefit from the vaccine.
30 / 185 * 11 = 1.7
1.7 ~= 0, so the sample size is too small to support the headline.