stretch有“拉伸，伸展”的意思，我们常说的伸懒腰stretch oneself就用到了这个词。这里的truth是被伸展的对象，也就是说事实被夸大了，做了些延伸的解释

to say something that is not completely honest in order to make someone or something seem better than it really is

为了让某人或某事看起来比实际更好而说一些不完全诚实的话;夸大事实，言过其实

He was accused of stretching the truth about how much he had helped in the project.

他被指责夸大了自己在整个项目中的作用。