You're right in that an element of capillary action is involved in the process. The usual explanation for how fluids flow through xylem tissue is to do with the interconnected process of transpiration. Fluids are taken in by the root hairs, into the roots, into the xylem, and moved up the plant through the hollow spaces within the xylem known as lumen, rather like a straw or straws. This link gives more information in regard to this process as well as phloem and translocation, but it's not the most technical link http://www.bbc.co.uk/schools/gcsebitesize/science/add_ocr_gateway/green_world/planttransportrev1.shtml
A more scientific explanation is to do with the nature of water/fluid itself, that is transpiration, cohesion, capillary action and adhesion, and that is explained more clearly here http://www.dummies.com/education/science/biology/how-plants-pull-and-transport-water/
Essentially, transpiration from the leaves acts like you or I sucking on a straw - the higher the rate of transpiration, the more fluid gets drawn up through the lumen in the xylem tissue to the leaves.
I would just add that not everything is entirely proven or completely known when it comes to living plants, any more than it is with human bodies; when I did my training years ago, we were told it was assumed there were plant hormones that caused certain things to happen, but only some had been proven to exist and named. Over time, of course, many of these suppositions and theories have been proven, but I'm willing to bet not all will have been. But for now, the explanations given in the links above are still taught today, regardless whether anyone has or hasn't actually proven they're 100% accurate.
Note: 'sap' refers to fluids found in both xylem and phloem systems, rather than just that flowing up the plant through the xylem tissue.