In which I question the NEX APS-C Shallower DOF argument

pmow wrote:

I keep seeing various conversations here and elsewhere casually dropping the fact that:

The larger the sensor, the shallower the DOF.

In researching several of the top google results, it seems as though the above statement is not really true.

Only when adjusting the distance to recompose is the depth changed; This is a result of a change in the field of view, which obviously does come from using a differently sized sensor with identical lens.

I love the NEX system and will continue to promote it for the reasons I bought into it, and represent it accurately. To that point, isn't the main argument for APS-C over smaller formats a little bit disengenuous? The zooms and primes are by-and-by, about the same equivalent.

My supposition is that most systems produce a range of lenses in roughly the same approximate focal lengths. I have no love for other systems, but at random let's use the Nikon system which I was convincing a friend to *not* buy.

The Nikon system has a 2.7x crop and ships with a 10-30/f3.5-5.6.

That's very close to the kit NEX zoom, in both FL and aperture. Considering that these smaller systems like mFT are making wider lenses to compensate, can we really make the bolded statement above?