The fact that it is not found in woods is taken as evidence that it is non-indigenous.
1640s, from Late Latin indigenus "born in a country, native," from Latin indigena "sprung from the land," as a noun, "a native," literally "in-born," or "born in (a place)," from Old Latin indu "in, within" (earlier endo) + *gene-, root of gignere (perf. genui) "beget," from PIE *gen- "produce" (see genus).
Native to a particular region or environment but occurring naturally in other places as well. The American black bear is indigenous to many different parts of North America. Compare alien, endemic.