If their contact with him gave no indication he needed further help or posed a danger, they would need permission to enter or search.

If they had reason to believe he was in danger or a danger to others they could enter to arrest/detain/make contact to ensure safety and anything incidental to that, but no more.

If you do so and you suspect that there is something illegal inside or going on, best policy is to just do the bare minimum to secure the person, get out and go get a warrant. That way your giving max protection of privacy and not nearly as likely to have the search challenged in court.

I suspect he knew just what he was doing by meeting them outside and playing nice.