I heard a rumor that if you modify the photo by at least 10%, it doesn't matter if it's copyrighted and you can use it however. Is that true?

Absolutely not. If you change a few things in a copyrighted work, or add something to it (or take something away), the copyright that protects the work stays in place. The right to make changes to a photo, novel, or other copyrighted material is reserved exclusively for the copyright owner (who is almost always the author or photographer that created the material).

On written material, as soon as words are on paper, they are protected by copyright laws. A photograph is copyrighted the minute it is developed (or for digital images, the minute they are downloaded onto a computer). Note that ideas cannot be copyrighted, only actual images or strings of text. So when you find yourself in Yosemite National Park, you can take pictures of the same mountains that Ansel Adams photographed, but you cannot use the photographs of the mountains that he took without permission.

The unauthorized use of a copyrighted work is called infringement. If you steal someone's copyrighted material and the copyright owner catches you and takes you to court, there are sometimes stiff penalties (large fines). And you'll probably have to pay the copyright owner's attorney fees. Attorneys aren't cheap either, so don't steal photos that aren't yours.