It's certainly true that a person's height varies according to the time of day. (As woofgang says, it's because the discs in the spine become compressed). Where I would disagree with the statement, in the original question, however, is the idea that someone is shorter when they're asleep. What actually happens is that the discs compress during the day (so we're at our shortest last thing at night). During sleep, the body is horizontal so that the discs are no longer under compression and slowly return to their uncompressed state. So, if anything can be said to happen about our height - or should that be 'length' when we're horizontal? - it's that we actually get taller during sleep.
This shrinking/growing effect is more pronounced in some people than others. Gingerflaps mentions a quarter of an inch variation. In most people it's probably closer to half an inch - it can be more. I certainly notice it when I'm driving. I always have to adjust the rear view mirror each morning because I'm slighter taller than when I was when driving the night before.
Chris