> for all this experiment to be valid to begin with,the idea that superpositions exist must be true, correct?

Depends what you mean by "exist". All that needs to be true - and is true - is that QM provides an accurate model of the experiment. For many of us, QM is just probabilistic mechanics; i.e. probability theory applied to mechanics[1], and so long as you maintain the distinction between (epistemic) probability space states and (ontic) configuration space states (something the article under discussion here unfortunately fails to do), no ontic existence of [superposition] states is ever assumed in the first place.

[1] More precisely, a natural and necessary generalisation of the classical, Kolmogorovian probability theory you might be familiar with (necessary because of the noncommuting random variables):

https://news.ycombinator.com/item?id=19315457

See also: http://blogs.discovermagazine.com/cosmicvariance/files/2011/...