IIRC there are 2 parts to immobilisation 1 is cranking the other is fuel injection. The car's immobiliser (or IIRC the CCU dependent of age) handshakes with the engine ECU and they determine if immobilisation should occur. The immobiliser controls cranking by giving an earth to the starter relay on successful handshaking, the engine ECU by enabling the injectors.
The cranking can easily be frigged by giving a permanent earth to the relay, I presume this can be checked with the ignition off if you don't know the car's history.
However, I'm not sure how the injection side works. I'm not sure whether the injection is only cut on successful start or not enabled during start/cranking. It might also be the fuel pump it does not enable rather than the actual injectors - so there could be some residual pressure that might enable a start?
So its possible its immobilised - but I agree, it is more likely to be something else. (Good) diagnostics on the engine ECU should tell you if it is immobilised.