Testing is overrated?

I'd say that this is wrong for two reasons. I think you're right that adherence to spec is important (if the spec says "Send an email" and the app doesn't, then something is wrong). But:

1. Within spec adherence, there is still good code and bad code. Is the code maintainable, understandable, secure? And was it written efficiently?

2. Sometimes the spec is wrong. Documentation isn't infallible, and software should change based on users' needs.