The SSDI is a reliable source. When people registered for social security, they had to present documentation of birth.
There is also the social security
As far as comparing ages on the SSDI and the WW1 draft registration, I wouldn't get too hung up on it. No documentation of birth was required to enlist. Boys said they were older because they wanted to go fight. Older men often put down a date that showed they were younger because they wanted to defend freedom, their new country, etc.
family from: Bielsko-Biala powiat Poland