Never messed with NEXRAD data, but--what, specifically, do you want to download?
The link to other APIs on the NOAA site 404s; you might see if they would fix that; it might have some other useful code. Then again, it might not which may be why it's broke.
Where's a definition of the format if you do download the file(s)? If you're interested in KMZ files, readgeotable in the Mapping Toolbox is documented to be able to do so...