Its your choice to beleive a diagnosis or not. If you believe that you can actually block the convertor with carbon soot or melt the ceramic core - then your engine would actually be blowing black smoke like an overly fuelled diesel.
Even diesel engine converters do not choke up so early, they can choke but only if the engine never gets up to speed to heat up the converter as the diesel engine has a very cool exhaust compared to a petrol engine.
In my experience with these Kei cars - Even with correctly operating parameters - driving it normally. i.e. take small roads onto Shahrah-e-Pakistan, turn to Sh Faisal corridor, then on Shahrah-e-Faisal. Scoot along briskly like you would in any normal car, they could only afford a max of 11 or 13 km/lit. And if for some reason your cooling system gave up while driving in excess of 100 km/h - you have less than 15 seconds to shut down - because the engine rpm is too high and the engine is under great stress.