I know there are studies claiming the curve is as safe as a fastball but I have yet to read a study where I could tell they measured everything they should have. For example, the first study mentions measuring moment forces on the elbow. They then go on to mention supination and pronation:
As mentioned, the forearm did remain more supinated and the wrist more flexed during the cocking and acceleration phases of each curveball as compared to the fastball but the supination velocity did not differ significantly implying that this was also not the cause of the increased injury rates.
But while they talk about "supination velocity", they don't say anything about the degree of supination. Nor do they talk about rotational forces created by the supination. And words like "implying" appearing in studies(bolded above) always cause me indigestion.
Now, I'll be the first to say I don't fully understand all of the terminology used in these studies. But I prefer to qualify the claims of the curve being safe by adding that the number of curves thrown should be limited to no more than about 20-25% of one's pitch total. And I also like to add that while the studies do mention using proper technique, it often requires the use of high speed video to verify proper technique is being used. It's not clear if or how this was done in the studies.