Lavin et al is the study mentioned. The results of the study support the claim that this water pillow improves neck pain. Another scientific article reviews this first study in its literature review and presents the following criticism:
... In [Lavin et al] there is no mention of a “washout period” between pillow administrations (to bring the subjects back to their base-line levels); without this, it is unclear whether there were any carryover effects between different pillows. Furthermore, the analysis appears to have utilized the mean of each post-treatment period, rather than pre-post treatment period changes, so it is not clear whether the cross-over data may not largely be the post-treatment data of the previous pillow.
To summarize this in plain English, the data gathering methods of the first study are poor. If the subjects sleep on a great pillow, and then on a mediocre pillow, the experiment may find that the mediocre pillow improves neck pain, when the improvement was actually caused by the great pillow.
The study was funded by Mediflow. Although scientic research is supposed to be unbiased, there is a significant bias towards finding positive results for people who gave the study funding.
This review article examined 127 scientific articles about neck pillows and their effects on neck pain. The Mediflow water pillow is one type of neck pillow. The review did not find evidence suggesting that neck pillows are helpful for neck pain. This conclusion is too general to specifically discredit the Mediflow pillow, but it doesn't look great either.
The evidence presented seems somewhat inconclusive.