Hi Jane, I'm not related, but took a look at the Rodmans.Question - Why do you think your James was born in Washington County?
In the 1850 census, there are 2 James Rodmans in Washington County, and there is also a James Rodman in Vermillion County. All are b. ~1826-1828 era.
James A. who married Francis Esther Kinnard on 3/22/1864 is in Buchanan Co. MO by 1860 and appears to be the son of Samuel b. ~1778 PA and Delila b. ~1794 VA. per the 1850 Washington Co. IN Census. His records consistently show James A. Rodman.
James H. Rodman married Rachel Harris and remains in Washington County IN.Based on his recurring close association with John F. Rodman, I'm guessing his parents are James b. 1785 PA and Elizabeth b. 1788 VA.His records consistently show James H. Rodman.
I think your James was likely b. Vermillion Co. and there are no records that show him with any middle initial, unless possibly a death cert for one of his children, that I don't have access to.There is an Alexander Rodman b. 1800-1810 in the 1830 Vermillion census, who has a son who is age appropriate to be your James.
BTW - I agree with you that any family tree that is unsupported by documented sources has no credibility, and can only be used for possible leads.Unfortunately, many people only copy someone else' info, whether it is right or wrong.