Personally, while such theory appears appealing from many reasons and we can see many connections to ancient Aether theories apparently, personally I'm in doubt, just the neutrinos are fundamental particles, responsible for gravity action, space-time (curvature) the less. By such theories neutrinos are considered to play role of gravitons or even Aether particles - i.e. much more fundamental particles, then neutrinos. Neutrinos are particle exhibiting a weak force, which is explained by AWT like manifestation of surface tension, analogous to repulsive force of tiny mercury droplets, which are composed by even much smaller particles. In addition, if neutrinos are forming gravity force, they should remain very invariant to it. Such neutrinos not only should pass the event horizon of black holes freely, their concentration should form the gravity field itself and gravity waves should be formed by waves of neutrino concentration. After then the event horizon of black holes should be formed by pure neutron fluid and black holes should be a neutrino stars. Inside of neutrino stars no gravity should appear at all, which violates the concept of daughter singularities inside them. While even AWT considers, some neutrinos could pass event horizon of black holes, observed neutrino flux emanated by black holes is generally much weaker.
In addition, the high density of neutrinos in vacuum brings another conceptual problems. By contemporary theories the mass of neutrinos accounts for some 5% of total mass of dark matter, i.e. the same portion, like photons of light. The neutrino gravity model would require such portion to become a much higher to explain a large gravity field, thus violating the concept of dark matter with repulsive behavior and gravitational lensing at the same moment.
In addition, high concentration of primordial neutrino flux makes the measurement of solar neutrino flux impossible, while we can still measure it with precision, sufficient for detection of neutron oscillations (we cannot measure the flux of water molecules, if such molecules are forming water at the same moment). From all these reasons is apparent, the vacuum must be formed by much smaller and more dense particles than neutrinos. Because we can see no apparent lower limit for Aether particle size, AWT is assuming, Aether particles are infinitely small, thus making Aether (particle field forming vacuum) universal, but abstract concept.
The neutrino based gravity theory can serve as an example of theory, which can be disproved easier by predicate logic, then by formal math, because it behaves in many aspects like epicycles theory of deBrahe, which supplies many predictions consistent with heliocentric model. Because of conceptual richness of Aether model, such emergent theory can even supply a new testable predictions, because it brings a new insights into existing model of gravity (a density gradient concept in particular). If nothing else, such theory is pleasant by its adherence to Occam razor principle, because it doesn't introduce a new concepts into physics - it just combines the well known ones. But as we can see on the example of Ptolemy's model (which follows the Occam's razor principle apparently) - even such approach can become misleading from less or more distant perspective.
Albert Einstein: "Everything should be made as simple as possible, but not simpler."