According to the researchers, it 'can' or might work; and that is why they're running a human trial: to determine whether it is even plausible that it does work. The University of East Anglia article on the subject says,
The researchers found that mice fed a diet rich in the compound had significantly less cartilage damage and osteoarthritis than those that were not.
[...] Researchers from the School of Biological Sciences and Norwich Medical School are now embarking on a small scale trial in osteoarthritis patients due to have knee replacement surgery, to see if eating broccoli has similar effects on the human joint. If successful, they hope it will lead to funding for a large scale clinical trial to show the effect of broccoli on osteoarthritis, joint function and pain itself.
[...] This study is important because it is about how diet might work in osteoarthritis. Once you know that you can look at other dietary compounds which could protect the joint and ultimately you can advise people what they should be eating for joint health.
[...] For the small scale trial, funded by DRINC, half the 40 patients will be given ‘super broccoli’ - bred to be high in sulforaphane - to eat for two weeks before their operation. Once the surgery has taken place the researchers will look at whether the compound has altered joint metabolism and if it can be detected in the replaced joints.
In summary:
- They decided that a testing shows that it works in mice
- They decided that sulforaphane is the mechanism/cause
- They're testing on humans (who were about to have joint surgery anyway) to see whether eating brocolli affects the level of sulforaphane in the joints ... because, they find plausible that it could or does work, if and only if they find that when humans eat broccoli then that affects the level of sulforaphane in the humans' joints.