There has been much conjecture, by investigating officers, press and the public, about Greenson's involvement in a possible cover-up concerning the circumstances of Monroe's death.
Terdapat sejumlah penjelasan, melalui penyelidikan pihak berwajib, pers dan masyarakat, tentang keterlibatan Greenson dalam kemungkinan penutup-nutupan puncak kematian Monroe.