During the 1950s and early 60s, there were a lot of exploitation films about wicked teenagers, such as BLACKBOARD JUNGLE, HIGH SCHOOL CONFIDENTIAL and even TEENAGERS FROM OUTER SPACE!! So it is not surprising that a plot like "Fun and Games and Party Favors" is used in THE FUGITIVE.
Richard Kimble is posing as Douglas and he works for a rich family, the Glenns. But Mr. and Mrs. Glenn are having problems with their daughter...but they don't realize it. Mrs. Glenn is trying to micro-manage her daughter's love life and it's not surprising that Joanne is feeling rebellious. But it's more than just token rebellion going on with this young lady. She is desperate to get out of the house and is trying to convince her boyfriend (who the mother does NOT approve of) to elope with her. As for Dan (Mark Goddard), he's actually a pretty nice guy and would much rather date Joanne openly and get her parents' permission to one day marry her.
In the midst of all this, Mrs. Glenn wants to throw her daughter a party...with the PROPER sort of young people. Instead of staying home to supervise, she leaves all this up to Douglas! This turns out to be a serious problem, as one of the jerkiest young men, Phil, has learned who Douglas really is...and is planning on using extortion to get him to allow him and his stupid friends crash the party. What's next? See the show.
While this all sounds a bit inconsequential, it's handled very well and the show worked just fine. And, it illustrates the familiar refrain of the day that kids run amok when parents are just too busy with their own fun to adequately supervise them.