What a fascinating mystery! Perhaps you can follow news reports from the time, if you look into newspaper archives mentioning that Purvis had gone missing. I found a similar situation in one of my great grandfathers, who went missing for a short while, and the news was picked up in the newspapers, which I was able to find copies of and include on his profile page here in WikiTree at:
Frank Sylvester Stieger
I was fascinated by the way newspapers at the time really took strong interest and concern about this missing persons report from 1898 in Saint Paul--and then, quite inexplicably, my great grandfather somehow turned up in North Dakota! This was not a story I'd ever heard from my father or his parents, so discovering all of the news clippings was truly amazing for me.
With regard to including source documents for Purvis, you can definitely at least include the Ontario Births, 1869-1912 records where he appears at:
"Ontario Births, 1869-1912," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:QV9H-P9WD : 15 January 2016), Purvis Charles Ingraham, 05 Apr 1909; citing Birth, Toronto, York, Ontario, Canada, citing Archives of Ontario, Toronto; FHL microfilm 2,394,459.
I see you already have the information from these records (such as that on 5 Apr 1909 Purvis Charles Ingraham was born in Toronto, Canada to John William Ingraham and Angella Collier), but what makes our WikiTree pages so wonderful is that we do include source records wherever possible, to indicate that there are facts to back up all the profile pages in our family tree.