"But we don't want them to force us into any false statements."

Making false statements to Julia was one thing, to her father quite another.

It would be beneath him to make any false statement.

And the best part is, you don't have to make a single false statement.

"No, but there is a law against giving false statements in a police investigation."

That - from Joe's analysis - had been another false statement.

We also allow that this could be a false statement.

Having never made a false statement of material fact to the corporation.

The center said she refused to make any false statements about its work.

So you do not have a paradox on your hands, just a false statement.