“Unless he came through the front door at the invitation of the person who answered the door, he was an intruder...”
Wrong. If he was invited by an adult resident of the home, he wasn’t an intruder, no matter where he entered the home.
“Did Dad tell her previously that she could not have men in her room? If he did, the guy was an intruder.”
Wrong again. If he was invited by an adult resident of the home, he wasn’t an intruder, regardless of what the “house rules” were.
Just to demonstrate how your thinking is wrong, consider if the police came to the house, and sought entry without a warrant. It would not matter if the father gave the daughter permission to let police in the house or not, as long as an adult invited the police in, their entry would be completely lawful.