This was my take, too, but since then, I read more about that accident, and it was less clear-cut:

Proactive not reactive | International Railway Journal

The accident occurred after the girls opened the manual gate and walked onto the tracks while the crossing sirens were still sounding. They thought the siren was for the Cambridge-bound train that they wanted to catch, and had already passed the crossing. It was at this point that they were hit by a second passing train that was travelling through the station from Birmingham to Stansted Airport. They were killed instantly.

A scathing analysis presented to the court by safety specialist Dr Tony Cox of the final risk assessment of the level crossing conducted eight months before the accident found that the assessment neglected to show that the level crossing in question had extremely short visual sighting times. The low-frequency of off-peak services also created an incentive to catch immediately departing trains, while the positioning of ticketing facilities on only one platform at the station meant that passengers often had to use the crossing more than once.

Cox estimated that there was a "near miss" at the crossing at least once a week, adding that the failure to warn passengers of the passage of a second train was a very significant factor in the two girls' deaths and a huge failure of the level crossing system in place.