Yes during a physical the doctor does check your private parts and will examine and touch your penis and testicles.
The reason the doctors touch your penis and balls or testicles is to feel for lumps to check for testicular cancer.
If the doctor feels any lumps in your balls or testicles then they may send you for more examination or have some blood work done.
Having your testicles and balls and penis touched by a doctor or seen by a doctor can be embarrassing however it's routine for the doctor and just a part of their job.