Is it true that the Government can deny a security clearance for something as simple as filing bankruptcy?
Yes, a security clearance can be denied for many reasons uncovered during the investigation reflecting the 13 criteria.
Remember, a clearance determination is based on whether or not you are trustworthy and stable. Any events or actions on your part that may subject you to release classified material to unauthorized personnel or prevent you from protecting it properly will make you subject to a decision to deny your clearance request.
The best advice I can give to you is to Be honest with all of your answers!