In the Catholic Church, especially in America, an annulment is practically the same thing as a divorce nowadays.
When I and my first wife divorced, I applied for and received an annulment. But, that marriage was short-lived, and there were no children. There was also (now, looking back, I can see it), the problem of depression. (Women are susceptible to this.) Plus, I had grounds. That annulment was legit.
When my second wife and I divorced, we had been married for several years, and had a children. Plus, depression was not involved, and it was a no-fault divorce. Therefore, neither I nor my second wife sought, nor do I think I, her or we would have been given an annulment.
All things considered, Kerry's case seems to be more like my second divorce. Yes, the woman suffered depression, but this, by itself, is not grounds for an annulment. That would be like saying that if the woman has a physical illness, that would be grounds for an annulment.
When you marry, you marry for "better or for worse, in sickness and in health." Mere depression is a risk you run when marryng another person. The Catholic Church should NOT have granted the annulment to Kerry. Either that, or the Catholic Church should accept the fact of divorce.
If it granted the annulment -- that's the question no one seems to have a definitive answer to. He's mentioned requesting an annulment, but weasels out of saying he actually got one.