When we run hack days we do simple things like check when the domain was registered, check if its indexed in Google and a few other things but what we also do is have at least two developers on the judging panel that can judge if someone has cheated or not... It does work both ways though, we almost lost a PayPal hack day last year because the judges believed we had worked on the product previously when we had genuinely built it from scratch in 24 hours.
I'm glad you guys weren't disqualified, but I'm lol'ing at the irony of PayPal judges presuming guilt and asking you to prove your innocence. Good to know that they carry that policy everywhere.