Sure, stats do matter for different skills. This is good, but it is not enough. There could be more of them. It's exactly how system in computer game should look like, it is complex. Simplicity is for non-computer games. Since computer is capable of making all the complex calculations, player don't have to focus on looking at all the factors (skills/stats/whatever), but only playing his character, like you live your real life (without looking at some stats). So if there are a lot of them and player gets lost while looking at them and figuring out, exactly which is used for what, it is even better, because player shouldn't do it anyway, to be capable of acting better as the character. Player know his character from his actions, not some written down stats.
What about accuracy? Will you make use if it when you switch from sword to axe? There is not even such an ability.
And you can train everything. There are no exceptions. Stat or not, you need to practice to get better in it. (only for "stats" in PS has not valid developing system for now). In fact the difference beatween stats and skills slowly disappear if you think on what i write. But if there is need to divide the "abilities" into two groups, it would be these which are gained only by practice and these you need some teaching besides practice.
Funny, this topic made me put all the different puzless together into correct, not flawed system. (yeah, i did not just write it all there ;P. I'm not sure i want to start another discussion to hear the same questions and doubts, from similiar threads ;P. If i will be lucky, i will give it out in bits instead, i gues)