The wording is clunky, I agree, but the meaning is clear (well, in my mind ). They are essentially saying that the voltage seen on that pin will be the same voltage that was supplied by the external power supply -- and that could be anywhere between 12V and 19V (though 19V is typical as the Intel-supplied power supply provides 19V). This is a roundabout way of saying that there are no voltage converters in the path between the two connectors.
You are correct; in the case of the NUC6CAYB, the connector, overall, is just there to provide power to attached device(s) (what they are calling "expansion peripherals"). This connector type is actually supported by a significant number of the NUC System and Kit products.
Overall, only those NUC boards that are sold as standalone board products will have an "internal" connector to support power input. The standalone board products are:
NUC7i7DNBE
NUC7i5DNBE
NUC7i3DNBE
NUC5i5MYBE
NUC5i3MYBE
DE3815TYBE
Note: My understanding is that, when you purchase one of these board products, no external power supply is included; you are required to provide this yourself.
The higher prices for these board products, as a result of their positioning as Extended Lifetime products, may put them out of your comfort range. In my opinion, unless the extended lifetime feature is of importance to you, it would be cheaper to purchase the NUC6CAYH (or its 7th generation replacements, NUC7CJYH and NUC7PJYH), pull the board out of the chassis and use it separately. It means adding a connector tip to your power supply output, but this is a lot cheaper than the alternative!
...S