I don't think they particularly have minute by minute timetables on the MRT, just first and last train times and number of trains operating per line during peak/off-peak periods. On the circle line the trains are driverless and operate with a moving block system (Comms-based Train Control), so the headway between trains is fairly constant, but the absolute timings are dependant on the train ahead travelling at the ideal speed, not stopping for too long etc. (e.g. if someone holds the doors to jump onto the train last minute you'll be delayed as the doors re-open and attempt to close again). So I think you would have to extract logs from the control system or the trains themselves to establish exactly where they were at any particular time. And bear in mind that this information is probably rarely used (at least for this purpose) and may not be in a format suitable for the kind of analysis they needed to do. Funnily enough it was the use (and failure of) of the CBTC system that caused this problem.

Also remember that until they begun the analysis it wasn't clear that a single train was the cause. I imagine they were investigating trackside issues as well as issues with those trains that stopped, rather than an independent train that wasn't experiencing problems.

TLDR; It's not a case of looking at pre-defined timetables.