It's not obvious, that's why we have clinical trials.
What is obvious is that if your research process tests everything in mice first, and only tests in humans what already works in mice, you will find many treatments that work in mice but not humans. (Any treatment with the opposite character - works in humans but not mice - gets discarded by your process and never tested in humans...)
Which actually seems suboptimal in a case like this. We know the risks and side effects of steroids in the human body pretty well at this point, and they're not not too bad. If I had muscular dystrophy I'd probably be willing to give them a shot, even if they didn't work in mice.
There’s a saying that it’s a great time to be a mouse with muscular dystrophy. It does seem like using mice as a model hasn’t worked very well, but I am not sure what the alternative might be (chimps?) or why researchers continue to use mice anyway. Edited to add: It would probably be emotionally/ethically more difficult to use chimps … they do some pretty awful things to the mice, making them run until they collapse repeatedly and then killing them at the end (for example).