Why wouldn't the life raft keep them out of the water? Even if they were wet when they got in it, I'd have hoped the raft would have enough cover to keep the wind and rain off them, and their body heat would eventually warm up the water in their clothes, and then they'd largely stabilise.

For example this at £600 was one of the cheaper ones I found when I searched. It has an integrated tent-like canopy and an insulated floor. Wouldn't something like that protect from exposure for many days?

In heavy seas you get water ingress into the raft. That can vary from a few millimeters to completely flooded. Also the raft will chill to ambient temperature. Not a good situation, even in ideal situations. The blunt truth of the matter is that liferafts are only intended to provide short term sanctuary for a few hours to a few days depending on the conditions.
Long term survival in a raft only occurs in tropical waters under unusual conditions.

It appears that in this instance the Crew had no chance to abandon. That strongly suggests to me that they were taken by a wave.

An excellent account of just such a survival is Steve Callahan's 76 day survival and recounted in "Adrift." I think most folks here are familiar with it. If not, I highly recommend it.

For the super short version, read his "5 Realities of Being Lost at Sea" here:
http://www.cracked.com/article_21145_5-things-i-learned-about-survival-while-i-was-lost-at-sea.html