This is only true if both you and your partner were sure neither of you had an STD before having sex. It is possible for you to only have sex with one partner, but that person may have had sex with several people, increasing the chances of having an STD.

STDs are spread through any bodily contact or by sharing a towel with someone.  

STDs are spread by sharing or transferring of bodily fluids. They are not transferred through hugging or shaking hands, or using the same toilet or personal belongings of someone with an STD. There are some exceptions to this. You can get syphilis by kissing someone if there is a sore in their mouth. You can contract genital warts by sharing a towel with someone who is having an outbreak and uses the towel.

Abstaining from sex until you are in a monogamous relationship where both partners have been tested for STDs and are sure they are infection-free is the best way to avoid contracting an STD. You should not be embarrassed about asking your partner about testing and STDs. It is impossible to look at someone and know whether or not they have an STD, these diseases have nothing to do with how a person looks, how clean the person is or how well they dress. STDs are sometimes noticeable in the genital or groin area but there are more times when no symptoms are visible. Take care of yourself by insisting on testing before beginning a sexual relationship.

References:

"Chlamydia - CDC Fact Sheet," Reviewed 2011, March 25, Staff Writer, Centers for Disease Control and Prevention

"Genital HPV Infection - Fact Sheet," Reviewed 2011, Aug 25, Staff Writer, Centers for Disease Control and Prevention

"Gonorrhea - CDC Fact Sheet," Reviewed 2011, Apr 5, Staff Writer, Centers for Disease Control and Prevention

"Sexually Transmitted Diseases and STD Symptoms," Date Unknown, Author Unknown, AVERT.org