I think your data is incorrect. I voted in Central Ohio, and they required a photo-ID from me prior to allowing me to vote.
Unless it is county-specific?
Ohio law §3503.16(B)(1)(a) and 3505.18(A)(1):
All voters must provide to election officials at the polling place on the day of an election proof of the voter’s identity. Also applies to voters requesting and voting an absentee ballot.
Acceptable forms of ID:
Current and valid photo identification, defined as a document that shows the individual’s name and current address, includes a photograph, includes an expiration date that has not passed, and was issued by the U.S. government or the state of Ohio
Current utility bill
Current bank statement
Current government check, paycheck or other government document
Utility bills, bank statements, paychecks, et al do not have photos on them.
For voters without ID:
A voter who has but declines to provide identification may cast a provisional ballot upon providing a social security number or the last four digits of a social security number. A voter who has neither identification nor a social security number may execute an affidavit to that effect and vote a provisional ballot. A voter who declines to sign the affidavit may still vote a provisional ballot.
Voters who cast a provisional ballot because they did not provide acceptable proof of identity must appear in person at the board of elections to provide such proof within the 10 days immediately following Election Day. (see the Ohio Secretary of State’s FAQ on provisional voting)
How strictly counties interpret or apply the law? Have to agree county by county depending on Election officials, poll workers etc...