This seems like a very strange definition to me -- is the statement "the dinosaurs were prehistoric animals" false?
No, it's valid, makes sense, and is an accepted term. Although it's strictly limited to the period before we have written sources, not before we learned to write (we could have written in sand for millions of years - but it's in our prehistory...). The period after is called "recorded history".
- definition modified to try to explain the usage.
Can anybody improve the "surviving records" bit, i.e., explain why a cave painting is not a surviving record?
- IMHO it pretty much boils down to "pre-writing" = "prehistoric", "post-writing" = "posthistoric"