No, they may not view your medical records. However, if they find out that you lied (or omitted important information) on your pre-employment physical, you may be at risk for disciplinary action including termination.
Whoever performs your pre-employment physical is charged with determining two things. The first is that you are free and clear of communicable diseases and have documentation of necessary immunizations and titers. The second is that you are capable of performing your job duties as laid forth in your job description. If you have had temporary back strains and are now recovered without any diagnosis of degenerative disc disease, then lifting should not be a problem. However, they are putting themselves at risk for worker's compensation claims if they hire you and you subsequently injure your back again.
Hospital systems vary in terms of what accommodations they are willing to extend to employees. There is one health care system in my area who is well-known for not hiring anyone with a history of back problems. They also refuse to grant light duty or accommodations, so that their employees end up being fired if they are injured and cannot return to full-duty within the time given under FMLA. However, many other employers are more understanding.
Good luck with your career