In "Observation of 8B solar neutrinos in the Kamiokande-II detector" (Phys.Rev.Lett., 63, 16(1989), http://prl.aps.org/pdf/PRL/v63/i1/p16_1) the Figure 2 shows that only small percentage of registered neutrinos came from the Sun direction. The rest of registered events have random direction. Can it potentially mean that majority of the registered neutrinos came not from the Sun? If not how this background noise can be explained?
That paper describes data from an early version of Kamiokande detector. Later versions can even take a picture of the Sun just using neutrinos: http://apod.nasa.gov/apod/ap980605.html.
The paper discusses various sources of background neutrinos. Whether it's worth going into the sources in detail is debatable since later versions of Kamiokande did so much better.