I am sorry I cannot help you with the Bennett name you are inquiring about. My great-grandmother was Celia Bennett from Virginia. Your people may well be from this group. Celia married William Kyle who served in WWI, France. I am looking for information on her (or him).
The name Greene is well known as a Melungeon name. These people are Native American, orignal Spanish or Portugese, etc. and are found in the southeast up to southern West Virginia, and came to Greenbrier Co., WV, where I live. They are mainly from eastern Tennessee, southwestern VA and Kentucky. These people were in the census as FPC or mulatto, regardless of nationality, until 1850 and then were allowed to call themselves Cherokee. Some "passed" as white in order to own land. They are extremely interesting and fairly newly discovered, a heritage to be proud of.