To me, it felt like the producers had cherry picked a journey that they suspected would have a high chance of going wrong, hence making the railway industry look bad. First potential issue is the first leg involved a CrossCountry service from Bristol to Birmingham, a route that is known to have overcrowding issues. Second, the interchange time at Birmingham New Street was tight (12 minutes according to the National Rail site), meaning even a short delay on the CrossCountry service would result in her missing the Avanti Birmingham to Edinburgh service. Third, Avanti are known for currently having a lot of issues with cancellations, so the odds of this service being cancelled were high. Therefore, given these issues, it is not surprising something went wrong on this journey.
I suspect most passengers doing that route by train would use the direct CrossCountry service from Bristol to Edinburgh, even if does take a bit longer.