Are you sure about “none” being singular in that context? I agree that the title is inconsistent, but I'd have written “None of us know what we're doing” (if I couldn't just pick some other phrasing).

gcide defines “none” as “No one; not one; not anything; – frequently used also partitively, or as a plural, not any.” and also offers “None of their productions are extant. –Blair”, both purportedly from 1913 Webster. So it seems that the pronoun can be interpreted in either number as needed.