This is one of many questions within Chinese Medicine that doesn't have a clear definitive answer. To come to your own conclusion on the matter there are some things to keep in mind.
First, there is a difference between saying it doesn't matter and saying a "precise" cun measurement with an expandable tape measuring device like how many are taught in schools is less effective than developing your own skill in palpating the proper point.
Second, there is clearly a difference between sham acupuncture and "real" acupuncture perhaps not as much in generalized pain cases but certainly as you get into more serious complex health issues.
Third, there have been a number of studies (search pubmed for these) that have shown a difference in the intensity of change in the body (whatever they are studying, brain activity, vascular changes, etc.) between the "same" point but needled millimeters apart. So from those it appears that it does matter, possibly even making a difference clinically - but there are no studies that I know of that technically differentiate between someone finding the point with an "exact" cun measurement vs. someone "feeling" where the point is.
My general sense is that the body is alive and the points are alive so I tend to stand on the side of increasing your own sensitivity and using that but keeping with the knowledge that you cannot just needle randomnly. As practitioners get more experience there certainly is a knowledge of where the points are without measuring - even just from familiarity but moreso from palpatory skills. That said, in TCM and in other systems, Tibetan Medicine, for example there are some very advanced, highly skilled practitioners that measure definitively every single time.