Yes, it is true. My daughter discovered that her freshman year. She is now a junior. I don’t know how sizable the homeless population is, however I do know she ran into most of it on portions of High Street. She never saw any of it directly on campus. That being said, I trust that she is safe and knows when to be out and when not to be. OSU is pretty much a safe campus as there are blue emergency lights everywhere as well as campus police. And, with the amount of students who attend, you are not likely to be out on the streets alone. Safety in numbers, as with anywhere. 
OSU is an excellent university, so try not to let this sway your decision. Your son will get an excellent education there. Good luck!