Sorry, but you're pretty well wrong on all counts - failed capacitors 'may' cause further damage, depoending which specific ones have failed - it's by no means certain. Also, as he stated that the set works perfectly normally after 5-10 minutes, it obviously hasn't caused any further damage in this case.
But more importantly, they don't 'go low in Capacitance', they go 'high in ESR' - and anyone involved in TV repairs for the last 10-15 years should have an ESR meter, it's an essential instrument these days.