'Counting' quicks and slows makes no sense. What is 'quick' and what is 'slow'? MAYBE it is a relationship to two movements, but dance isn't based on that - it's based on a relationship to music and movement. What beat and what movement happens is real - 'quick quick slow' is relative to - whatever - and that's why most beginners see ance as a 'basic step' of quicks and slows, and most dancers past the beginner stage see technique related to quarterbeats of music as the way to 'define' movement. That's why beginners can always seem to 'count' the same QQSS or whatever to what they see - they are not aware of where the movement starts (on 1? On 2and / a?) or where the accents and such are.
You'll always lose an argument with a beginner about timing - they cannot see anything past what they know, and what they know is long and short 'steps'. Try to explain that, for instance, Int'l starts on 2, and they will blithely start 'counting' on one, missing the body action on 4/1, the accent on 2, etc.
'American Style' was created at the beginner level to be comprehendable to... a beginner. Int'l does not pander to this - the movement you start out with is the movement you can do championships with. However, the average social student simply sees a box shape and a slow and quick pattern, and believes they have 'learned' rhumba in the 4 to 6 weeks of their course. To them, what YOU dance is 'wrong'...