What happens on the Internet stays on the Internet.

That truth was laid bare on Thursday, when Snapchat, the popular mobile messaging service, agreed to settle charges by the Federal Trade Commission that messages sent through the company’s app did not disappear as easily as promised.

Snapchat has built its service on a pitch that has always seemed almost too good to be true: that people can send any photo or video to friends and have it vanish without a trace. That promise has appealed to millions of people, particularly younger Internet users seeking refuge from nosy parents, school administrators and potential employers.

But the commission charged that there were several easy ways to save messages from the service, and in settling the accusations, the company agreed not to misrepresent the disappearing nature of its messages.

The company’s early popularity and hype led to a multibillion-dollar buyout offer last year from Facebook, which Snapchat’s leaders spurned in the hope of something better. But the settlement announced on Thursday set a different tone, one that could extend to the many other start-ups that promise security, privacy and anonymity as an antidote to the public nature of Facebook and Twitter.