Very specifically: The statement of the article, ``Of course, there really ought to be an asterisk attached to that statement of the Equivalence Principle, because there are, in fact, some ways you can distinguish between gravity due to a nearby massive object (like a planet) and “gravity” due to acceleration.'' is, simply, wrong. The illustration preceding it is, just, misleading.
The statement claiming a distinction between `` the Coriolis effect, that would let you distinguish between the sort of gravity you get on the surface of the Earth and the fake gravity created on a rotating space habitat.'' is, similarly, wrong-that's the whole point of general relativity, in particular, and its generalizations, that reduce to it-that any such distinction is meaningless. While such a distinction was, indeed, possible in the Newtonian approximation, it turns out to be empty of content when realizing what the possibility of being able to perform a general change of coordinates implies. The terms ``artificial gravity'' or ``fake gravity'' , are, precisely, Newtonian misconceptions-they don't make sense, anymore, because there's no way any experiment can give them any meaning. It would be a very good idea to promote avoiding them.
Gravity beyond the equivalence principle can only mean what was mentioned previously: additional fields, beyond the metric, that don't couple directly to matter:, and can't be attributed to new forms of matter, but, only to properties of spacetime: scalar-tensor theories or supergravities-eventually with broken supersymmetry, it's the field content that matters. Scalars provide additional attractive forces, vectors additional repulsive forces (a remark made by J. Scherk in the 1970s, http://inspirehep.net/record/142417
). Spinors require more care.
There are ongoing experimental programs that attempt to place bounds on the contributions of such additional fields.
For a recent overview: http://relativity.livingreviews.org/Articles/lrr-2014-4/
The statement about straight line motion is, misleading, too, since motion in free fall, in any spacetime, is along the ``straight line'' in that spacetime-if there are non-inertial forces present, it's not, however-and that has consequences, that have been measured many times, in all sorts of ways.