What’s the problem with having applicants sign a ‘declaration of no criminal activity’?

Q: “We recently started making provisional offers to applicants, and we give them a form to sign that is a ‘declaration of no criminal activity.’ The reason we are doing this is because the hiring process takes so much longer when an applicant’s criminal background comes back ‘under review.’ So now, after we make the provisional offer, if the report comes back ‘under review’ we can still move forward with them and as long as it comes back clear or with items that are within our state regs (we are an elder care company), there should be no problem. If someone comes back with something on their record that we are not able to accept, is it okay to tell them we are rescinding the offer based on that, especially as they signed the form stating they had no criminal activity? Could there be consequences to the organization?” –Anonymous, Pennsylvania