Online petitions have had a terrible reputation for several years, and for good reason. It is too easy for anonymous people to sign.
When petitioning in person, outside of a supermarket for example, the person collecting signatures would need to be explicitly fraudulent to add non-existent people to the petition. This does occur but only in rare circumstances since this person is not inherently anonymous, this provides sufficient deterrence to fraudulent behavior.
Online petitions, such as We the People on whitehouse.gov, are notoriously easy defraud and have subsequently reduced impact as a petition. With only a CAPTCHA and a valid email, a single zealous individual could sign multiple times using any number of temporary email addresses available on websites such as 10minutemail.com