There's no such thing as a perfectly flat response, but that's not what you need: what you need is response flat enough that it is within human ear resolution.

(As far as I remember, headphones are actually harder to get precise response curves due to the interaction with the skull and precise physiology of the listener, but I may be mistaken in that.)

The problem with any claim from people that they can "easily" tell two pairs of headphones apart or two pairs of monitors apart is that most of the time these claims are not scientifically validated. There are numerous biases and gotchas involved in measuring audio fidelity, and one must be aware of these when designing experiments. (And the whole "audiophile" industry is based on the idea of selling snake oil technology to people with fat wallets and who think that they have better ears than anyone, and they go to great lengths towards denying the science.)

Likewise, it's very easy to write off actual observation as "bias" when the test isn't "scientific". That's one of my big gripes with what I thin of as the right wing of the hi-fi industry... the idea that human experience can be reduced to measurable and mechanically reproduceable observation in all cases. This reaction leads to "blame the observer" rather than questioning whether the scientist actually understands the problem domain or the question they're asking sufficiently well. It's every bit as emotional and reactionary as the "left wing" hi-fi subjectivists. But at least the subjectivists are owning up to their magical thinking.