Yes, it's quite normal for just one overnight to produce sufficient data to make a diagnosis. My diagnosis over 12 years ago was based on an overnight home study! It may seem a very small window in which to collect such significant results, but believe me, you won't even be aware of what it can detect!
There are always statistics that can be applied to any group ... eg weight, sex, hair colour, age, preferred brand of chocolate or tea etc .... and we know that they can always be massaged in favour of an argument ... so don't worry if you don't fall within the 'expected' sample!!! All sleep apnoea sufferers need diagnosis and treatment regardless of their vital statistics!!