I forgot to mention that the road was uphill, in that case was the coefficient of friction higher because the slope exercised an "additional force"?
Oh yes, the slope will be another factor. This is not because it provides an additional force, but because it decreases the strength of the normal force (that of the ground pushing up on the car, to balance the force due to gravity), which decreases the maximum strength of friction that we can have. The normal force follows the cosine of the slope: [math]
. So with the road angle the max safe speed is [math]
Road slopes are kept to fairly shallow angles and so this isn't a very big correction. At 10 degrees the max speed is reduced by only 0.8%, and even for some of the steepest roads at ~20 degrees, it's only 3% less. But it is another factor which acts against us for safely taking the curve.
So I think the best answer for what happened is a combination of effects. Being too close to the maximum safe speed for the curve with a slight uphill made it easier to lose control and harder to regain it, and control was probably lost due to braking.
There is a lot that can be said on braking itself. It's a bit counter-intuitive since you'd think it just slows you down and therefore makes you safer. But the problem is that by braking on a turn, you're trying to get an additional acceleration out of your tires, at the same time that they are already providing an acceleration in order to follow the curve. Any acceleration with the car requires friction, and as we just saw there is only so much that can be applied before you lose traction and start to slide. This is why we don't want to have to brake during the turn, but rather before we go into it, so that we can just coast through the turn. If you do need to brake, then it's best to apply them gently, and try to feel for that limit where traction is being lost and not push beyond that.