The study isn't (directly) studying sleep so that's hardly a surprise. It's perfectly possible that it's actually the disturbed sleep causing the response, and not the caffeine itself (at least from my brief skim of the paper).

Personally I place little to zero value on these "we asked people to estimate something and then found a correlation" studies, there are too many potentially confounding variables to account for. Perhaps the non-caffeine drinkers have different types of occupations, social class, health consciousness etc.

Yes, it’s very likely people with sleep trouble (caused by apnea usually) are more likely to consume greater quantities of caffeine to help fight daytime sleepiness caused by the apnea.