> At the end of his news conference, [Gov. Mike] DeWine said he didn’t authorize the arrest and reporters have “every right” to report during briefings.
> “If someone was stopped from doing that, or told they could not do that, that was wrong,” DeWine said.
Seems OP's statement is a bit generally misleading statement for a single incident, without also knowing the full details that prompted the arrest in the first place.
Things like "he was told to stop speaking during the governor's remarks" and "asked Lambert to stop his live reporting because they believed it was loud and disruptive" seems to indicate it's a situation escalating because ... I don't know, I wasn't there, and there doesn't seem to be any footage of these incidents. Hard to tell who is "at fault".
A single journalist, among many attendees, being arrested for allegedly being loud in a gymnasium during a news conference is a bit of a stretch to state as evidence that authorities are generally arresting journalists reporting on the derailing.