I would be fairly comfortable travelling to Krabi, Phuket, and Phang Nga. I, myself, would probably travel to some of the areas they advise against, but to this day, I haven't. If it's touted as a hazard, I'll often go the other way.
I'm not aware of any instances in the many years of the troubles in the south that were directed at tourists in these three tourism based provinces. Although blamed on religion, I think the southern troubles brew from money, power, and the like.
kpc, it's impossible though to know exactly what will happen with the violence in the south of Thailand (that has been escalating as of late). I'd hate to recommend anywhere that may present a danger.
The deep south of Thailand has genuine problems. The bombs, violence, loss of life, and other hazards are not commonly directed at any foreigners, but some foreign lives have been lost. You may want to think twice before going to Yala, Pattani, Narathiwat and Songkhla as recommended.
As is often the case in Thailand, things are never as simple as they first appear. Troubles in the Deep South will continue for the time being. But the Thailand I know is pretty darn safe. I keep my nose clean and have had no troubles. I'd expect anyone living similar would have similar experiences. Come and enjoy... it's a lovely place to holiday.