Open Question: What should I do if I was offered the job subjected to reference,employment history checks? (with fake info.)?

I was offered a job with quite a good pay package for my profile but some of my info was misrepresented e.g. stretching my employment history(over a year), salary. The job period that I over stretched has no direct relevance to the one I was being offered, but the HR required me to provide an annual income statement of my previous year and previous employer's email which I simply couldn't provide. SHOULD I COME CLEAN WITH IT AND HOPE THAT THE COMPANY IS WILLING TO REVIEW MY APPLICATION AGAIN KNOWING THAT THIS POSITION IS OPENED TO FRESH GRADS ALSO MEANING MY PAST EXPERIENCE IS NOT THE MOST IMPORTANT CRITERIA?