To go the route they've gone means they've been cleared from Cambridge to Hornsey, just for this purpose, though? And needed paths across the Digswell Viaduct.It may just be a paperwork issue, the train may be able to run on a line just fine but that needs to be checked. There are no ‘standard’ parameters, all train types must be passed specifically for running on each line. That includes being physically within gauge and also any potential signalling interference etc. The latter may permit them to be hauled only. The electronics on modern trains are a world away from class 309 units.
Avoiding the congested North London line and Finsbury Park area may well be a consideration too.