Just to be clear, what statements of Herodotus' is it that everyone is accused of doubting, and what arguments did he make in support of those statements?

There's plenty of Herodotus' Histories that scholars are nowadays pretty confident is inaccurate, regardless of his proximity to events. For that matter there's plenty of Histories that his contemporaries thought was inaccurate.

I don't really see the issue - am I to assume that Jesus rose from the dead because Matthew the Gospel writer says so, and the passage of time can hardly grant me more authority to say otherwise? Is that actually how we do history?