I checked several of the attorneys they listed and they did indeed seem to be licensed lawyers who represented veterans in such claims. I haven't checked them all, and you should always pick a lawyer
with as great care as you would pick a doctor, but this looks like a good place to start.
This website lists lawyers according to their state, so you can just
scroll or Control-F down to your state to see those in your state.
The list of state abbreviations at the top currently appears to be broken; I'll email the site admin to see if that can be fixed, but for now, scrolling should work.
Note For Lawyers:
If you are a qualifying lawyer, you might think about getting youself added to the site. Why not? It might steer some people your way.