Laying out what "used to be" and what "appears to be now" - here are the evidences that were originally brought:
- Wikipedia - previously said father wasn't in the picture and still pretty much shows the same thing.
- Find a Grave - used to and still does say that his parents are Capuran and Argint
- Holy Cow, his biography - while his statements are fuzzy, he seems to believe that his father was Carabina, but he says he barely knew his father and the statement seems to be shadowed by faint memories only and not much evidence
- The fact that Capuran didn't marry Anastasia until 1926 is a compelling argument. If it was 1916 it would seem to be more likely that they could have had an early child and just married a bit later. But that's a pretty big gap.
- The 1920 Census has mother's last name as "Corabina", which seems an awful lot like Carabina and not much like Capuran. She says she's "married" at that time, although her husband isn't listed.
- While no marriage records seem to be available between Carabina and Argint, it does seem a bit more plausible that they married around 1912-1914 (just prior to WW I) and he sort of floated in and out of their lives over the next decade until she finally divorced with him, probably due to neglect more than anything else. When she applies for the marriage license, she claims (on 10 Sep 1926) that she is currently single, unmarried, and eligible to marry.
That's about as much as I've been able to piece together without really digging in. But since I'm not the expert and Harry's a bit of a beloved legend in some circles, I wanted to make sure this got some eyes on it other than mine as there may be someone out there who knows something new - like Capuran and Argint had an affair, or knew each other years before they were married, or something that might lead to Capuran actually being "potentially" the father.