Dangit, I'm proud of myself. The FAA inspector is WRONG.
Found it :
E. Make and Model or No Passenger Limit. Some foreign CAAs (e.g., New Zealand and Australia) issue PPLs that limit the pilot to a specific make and model of aircraft or limit the pilot from carrying any passengers. Those persons must also comply with the make and model aircraft and passenger carrying restriction of their foreign pilot licenses when exercising the privileges of a § 61.75 U.S. pilot certificate (refer to § 61.75(e)(3)).
Here is the reference:
http://fsims.faa.gov/wdocs/8900.1/v05%20airman%20cert/chapter%2002/05_002_014rev1.htm
The easiest option for your friend is to take the written test, the required training and pass a checkride with a examiner for a "full" FAA PPL (H)
Otherwise a Jetranger "type" will need to be added to the EASA certificate.