Did you use auto activity start or did you manually start to the logging? It is always better to manually start the logging. Then you are in control when to start and stop the logging.
That's correct, Strava does not allow the distance editing. If the 1 missing km is really important to you, you could export the file, edit it with an external tool, delete the original from Strava, and then import the edited file. On my mind, it is not worth of the hassle. Personally, unless it happens frequently, I'd just ignore it. What you can do on Strava, is enabling the "Distance correction" available in the activity menu on the web version - it may add some extra distance, and even if it does not, you can reverse it.
