No, I'm not referring to Bonferroni's correction, which obviously has nothing to do with what we're discussing. I'm sure I've heard this called Bonferroni's principle.
Edit: Yes, in the section 'Statistical Limits of Data Mining' in the book Mining of mMssive Data Sets it's called Bonferroni's principle.
You typically use the Bonferroni correction when making general statements about a statistical relationship. You wouldn't use it for checking if a particular image shows illegal content. If you kept testing with your image classifier, your significance threshold would need to be continuously lowered and you would asymptotically reach zero.
Relevant XKCD: 882