Coils failure has been a longstanding issue with VWs and Audis built 2001 - 2004. It alone is why the original model Audi TT got such a low ‘Which?’ reliability rating. So this Audi dealer is either plain stupid, ignorant or is simply lying though his teeth to you. The reason for the failures is VW/Audi beating its supplier down to a low price for the coils that meant the supplier had to reduce the insulation on them. When the insulation breaks down, moisture gets in and the coils fail. Your car or might have been built at a time when VAG’s coil supplier had to treble production to replace the duff coils on cars on which they had failed. If coil failure leads to a misfire that then spikes the catalytic converter then the expense gets even greater.