As far as I know, there is no reason for a difference between whether the woman says she is divorced or she says she is widowed, and she is believed according to what she says.

There are two main reasons found in the Mefarshim for why we believe someone who has a Peh she'Asar. Some say it is a kind of a fortified version of a Migu, and since if she would not give us the first piece of information, we would never know she was married and forbidden to marry someone else, so she is believed now since if she is lying, keeping quiet would have acheived for her the same result.

Others say that in a case that a person gives us the whole story, he is considered the "Ba'al" ("owner") of the story, and the details are part of the whole story. So, although the story starts with her being married, but it has a detail to it that she also got a divorce, she is believed.

Either way, if the story she tells includes death or a divorce, she has a Peh she'Asar.

Kol Tuv,

Aharon Steiner