For one-way markets what you have is true. For round-trip markets, typically internationally, what you have is not.
E.g. LAX-NRT on 3/2 on UA 32 is $966 right now. Add a return flight on 3/9 and the flight _drops_ to $893.
I'd be surprised any airline gave you flak for telling them you were missing a segment. They might try to charge you more (!).