Actually, Yesterday's Enterprise employs the multiple timelines concept. Natasha Yar's presence on the Enterprise-C in the prime timeline is analogous to elderly Spock's presence in the alternate timeline created in the 2009 movie.
The Enterprise D changes, which wouldn't happen with multiple time lines. With the multiple timeline concept there would be a timeline where things had changed but you wouldn't have any knowledge about it, which Guinan does. Sending the Enterprise C back wouldn't change the state of the new time line either, as the events had already taken place. All you could do at that point by sending it back is create another time line.
In fact Natasha Yar suddenly appearing seems more likely they were thinking that there was only one time line. Spock appeared because he travelled from the future, while Natasha appeared because past events no longer happened.