You may check to see what version the UG file is saved under, my experience has been that there is a slight lag in newer releases support with the third party import options.
have them send you a exported parasolid file, I always ask for both just in case they have some weird setup in the native UG format. or like some due in SW happen to send the temp file instead. look at the file size of the UG, if it is around 1k or has the ~in front of the name it's a temp file. also what version on UG or is it Seimens NX6 or NX7 remember they are not UG anymore.
from the help file NX5/6/7 are not supported:
You can import parts and assemblies from Unigraphics II version 10 and higher, including import of Unigraphics NX 4 files.
NX7 & earlier versioned files can be opened in SW 2010. Is it possible that the NX part file you got is only a drawing file or an assembly file.If it is an assembly file, then the part files will need to be available as well. If it is a drawing file there will be no parasolids data to import. Remember that NX files are all *.prt files regardless if they are drawings, parts or assemblies.
I believe it is a part file but it may be an assembly as it has two solid bodies.
The part is also likely to have a spline that is imported from an external text file. Would these coordinates be embedded in the part file or might that be the missing data?