Remember one thing, Indus Motor is an assembler, not a manufacturer of Corolla. They put in your car what they get cheapest from Japan (mostly old discarded stuff).
When they were introducing Corolla, drum breaks were not available for that particular model, so they got discs.
Even Old Civic Exi had four-wheel disc breaks in the last few months, after which it was discarded, but it does not skid like Corolla on hard breaking at high speeds even with General tyres.
To control a Corolla, you should never push the pedal hard as it suddenly locks tyres (which means break is overworking). It skids because front shocks are hard and do not aborb momentum much that's why when wheels are locked body is still pushing ahead, thus skidding.
Solution. Be soft with breaks. I am driving a Corolla for the last 2 and half years and apart from occassional skids, it has never put me in any danger.