Following wrong lines: the (not so) Kennedy connection

I've had a couple of examples within the past year where I have found that I'd been following wrong lines. One example of this is my great-grandmother, Mary Elizabeth FITZGERALD.

I had been told that she was a first cousin to Rose Fitzgerald Kennedy; when I found a Mary E. Fitzgerald, born in 1883 who was the daughter of James Thomas Fitzgerald (a brother of Rose's father John Francis "Honey Fitz" Fitzgerald) I thought I had confirmed this.

I was a cousin of the Kennedys! Never mind that I can't stand this family, I had famous relatives that I don't have to go back 7 or 8 generations to get to.

Well... not so much.

You see, the Mary E. Fitzgerald who was the daughter of James Thomas Fitzgerald was not my great-grandmother. I came across a marriage record, courtesy of FamilySearch.org, of James T.'s daughter to someone not my great-grandfather. I then found, at the same source, another marriage record there for my great-grandmother Mary Elizabeth's marriage to my great-grandfather, and her parents are listed there as being Thomas FITZGERALD and Rose KILEY*. Her death certificate also gives the same names for her parents.

Thus far I can find nothing else on Thomas and Rose (Kiley) Fitzgerald.

Mary Elizabeth may well be somehow a cousin of the Kennedy Fitzgerald family, but if she is, it's through some other connection.

* Update: the name "Kiley" is actually "Connelly"

Ancestry chain:

Thomas FITZGERALD m. Rose CONNELLY

Mary Elizabeth FITZGERALD (1879-1954) m. David Thomas RYAN 

Clare Regina RYAN (1911-2001) m. Bernard KRANTZBERG 

My father (living) m. S. HOWES 

Me (b. 1974)