In theory, accordind to ICAO doc 8335, checks should be carried out on commercial aircraft only.
I found on EASA website this:
"
The principles of the SAFA Programme are simple: in each ECAC State, foreign aircraft (ECAC or non-ECAC) can be subject to a ramp inspection, chiefly concerned with the aircraft documents and manuals, flight crew licenses, the apparent condition of the aircraft and the presence and condition of mandatory cabin safety equipment. The references for these inspections are contained in the Standards of ICAO Annexes 1 (Personnel Licensing), 6 (Operations of Aircraft) and 8 (Airworthiness of Aircraft)."
And I think they normally check private operators as well.