It's not about voting-- it's about counting the votes. They take the frigging provisional ballot to determine if the voter is a valid county resident for purposes of local issues. If not, then you don't count their vote for local issues or candidates (even statewide if that's what Ohio regs say--although that would be suckful, imho)...then they COUNT the votes for the presidential (and Senate, if HAVA specifically applies to that too) race in order to comply with HAVA -- Voi-friggin-la. How difficult is that?
I refuse to believe that it is impossible to construe these two laws in concert so that effect is given to the intent of each without undue crossing of traditional state vs fed powers boundaries -- which is generally the rule in statutory construction and conflict of laws/federal pre-emption cases. (If they're actually going to prosecute people for a Felony for trying to vote when they moved more than 30 days before the election and thought they were registered....well, I have no words...)
I'll get more on the specific statutes involved, but here's a link to the Ohio League of Women Voters press release on the lawsuit, which is a good explanation.
http://www.lwvohio.org/advocacy/press/sos2.html