Agreed, but...
100% disagreed. For example, a Tube Screamer is all mids, and it's got to be one of the most blatantly pedal-sounding, least real-amp-sounding overdrive pedals I can think of. And I love Tube Screamers, BTW.
"Tube-like" is more than a matter of EQ, be it pre or post distortion.
FWIW, a Klon isn't all that Tube-like on its own to me either. But the way it interacts with tube input stages because of the way it's EQ'd, the way it blends the clean with the distorted signal, and the way it has TONS of output volume to really drive the input of an amp is very desirable, IMO. Especially for mid-gain applications.