Wherever/whoever you heard that from, they are lying to you, and you should keep that in mind the next time that source tells you something.
So, WHY ISN'T BIDEN on the OHIO BALLOT?? DO TELL!
Trump's name isn't on the ballot either because NOBODY is on the Ohio ballot right now. The ballot doesn't even exist yet. Ohio law said that the parties had to submit their nominees to be on the ballot at least 90 days before the election - by August 7. It is only after that date that the ballot is finalized. Trump's name hasn't been submitted yet because he won't be the official nominee until the delegates vote at the GOP convention.
That wouldn't be a problem for the GOP because their convention is a few days before that date, but the DNC's is after. So, people anticipated that could be a problem for the Democrats, and that Biden's name might not be on the ballot unless something changed.
Now, the truth is the Ohio legislature has moved that date in multiple elections in the past to accommodate major party conventions, and it has never been made an issue. But, someone got the dumb idea to refuse to do that this time for the Democrats.
The Democrats, who were desperate to avoid the horrible optics of Biden being nominated with riots outside their Convention, happily seized the opportunity, and their delegates are voting to change the nomination to be via an online meeting prior to that date. The Ohio Legislature, realizing they screwed up, finally agreed to change the law. But too late - the Dems are not going to have a live, in person nomination in Chicago, and we handed them the excuse to do that.
So, both Biden and Trump will be officially nominated prior the deadline, and both will be on the ballot.
You are a rude DEMOCRAT.