Hi portybelle,
The death certificate also details his parents as John Davidson and Margaret Wilkie, but as I understand it these details depend on the informant knowing. So while it's almost definitely correct, there's that very slight chance of it being wrong.
When Alexander first appears on the census (in 1861), his place of birth is given as "Scotland Aberdeen". But as he's living in navvy huts, and locations for other people on the same page are very non-specific, I'm not surprised at the generality. But I'm sure it's him as he does a lot of work on the railways through his life, and moves for the work. As far as I know, I'm the first one to find Alexander before his marriage in 1869 (in Monikie, Angus).
On the 1871 census, his place of birth is detailed as "Aberdeenshire Peterhead". From the other trees I've seen, this is where everyone assumes he was born. However in 1881, his place of birth is detailed "Aberdeenshire Cruden", as it is for 1891 and 1901. So I'm confident that's where he was born, even though every other tree states Peterhead.
I've spent the last few hours collecting all the Davidsons born in Cruden Bay (from Family Search). You're right, these are all very common names in the area and along with the name Gilbert, they make up about 97% (without counting!) of the male name born in Cruden Bay between 1709 (first appearance of Davidson born in Cruden Bay) and 1870 (as far as I've gone so far). I've collected all the names, and I'm trying to make some attempt at piecing together what I can of the families.
I also need to find out what I can about Wilkies, and especially Margaret Wilkies.
What I did discover, and something I think strengthens the case for Alexander belonging to this family, that William (son of John Davidson and Margaret RAINY) marries a Mary Mathew and uses the same male names:
William
John
(Mary)
Alexander
Thomas
George
(Margaret Jane)
Thomas (presumably the other Thomas has died)
(Janet)
James
Note the addition of Alexander, the one name missing from his father's children. Of course, it really could be just a coincidence! But given the other names all come from somewhere, Alexander must too. Furthermore, it's the third name used (i.e. not at the end). (Mary Mathew was daughter of Andrew Mathew and Jane Smith, no Alexander there.)