Thinking they sounded pretty interesting, I started searching to see what I could find out about Willy and Izzy (what? You don't give your ancestors silly nicknames?) and here is what I found...
"Alexander Montgomery, the fourth and youngest son of William of Brigend and Isabel Burnett, is thought to have died unmarried." -- Colonial And Revolutionary Families Of Pennsylvania, 2004
Colonial Families of America (1911) and A Genealogical History of the Family of Montgomery: Including the Montgomery Pedigree (1863) say the same thing, though the wording is so similar, the earlier may be the source for the latter (not having easy access to the full text, I haven't checked).
Genealogy: A Weekly Journal of American Ancestry from 1912 says that all of Willy and Izzy's kids were born in Scotland before they came to America 1701-02. My Alexander seems to have been born in 1705 (though I don't have evidence of that, either).
Sooooo, I start looking at other family trees, and virtually EVERYONE has Willy and Izzy as the parents of the Alexander that eventually leads to me. And NONE of them have any sources listed in the public trees! So, I started emailing them and just asking where they got the information and if they have any sources and I share the above with them so they know why I'm asking. Guess what answers I've gotten so far? "I copied it from another tree."
This is a real let-down because there is a lot of information about Willy and Izzy that is really interesting! I've enjoyed reading it, but it's not quite as exciting as when I thought they were my ancestors.
So, I'm backing up. I have a strong chain up to Alexander's grandson (Alexander III), but I'm going to start with him and see how much I can find. Given that he is a "third", I am fairly certain his father and grandfather are also named "Alexander" but it's not exactly an unusual name and I need to make sure I've got the right Alexanders.
So warning to all other noobs out there! It doesn't matter how many people have the same connection on their trees, if there's no documentation, don't copy it!