When all the ballyhoo was going on about drowning polar bears, there was submarine volcanic activity in the Arctic Ocean.
Blaming volcanic activity on melting ice is bassackward, imho.
Many moons ago, when people considered the internal heat of this planet the result of nuclear reactions at the core, a colleague and I postulated that the natural reactor at the core would poison itself when the daughter products reached a concentration sufficient to inhibit fission. That concentration (iirc) is fairly low, just a few percent. This would cause a period of quiescence which would allow the material to density stratify (removing daughter products), and then a resurgence when it did, which would account for the cyclical nature of the thermal cycles which drive tectonic activity.
No natural system is ever as 'pretty' as a theory, and the process would be unevenly distributed laterally in the layer of heavy metals near/at the core, but that might account for the thermal pulses apparent over geologic time, delayed and distributed by convection cells in the mantle.
Anyway, melting ice is one symptom of higher heat flow, not the cause thereof. There are other causes, after all, the ice has thermal interfaces on the top as well as the bottom, whereas heat applied from the outside is unlikely to cause volcanic activity without melting a lot more than ice.
The other as yet less than fully understood factor deals with cosmic impacts, and while causation is as easy to blame on cosmic impacts as more humanoid extraterrestrial influences (joking), if one was enough to cause an ELE at the end of the Cretaceous, other, lesser impacts could certainly cause less than ELE climate shifts.
Theory of the possible impact-related formation of the Carolina Bays may account for the Younger Dryas cooling. Either that, or all those Mammoth were cruising the glacial margins in SUVs again. (again, joking).
Melting ice requires the absorbtion of tremendous amounts of latent heat to achieve the phase change, with the effect of cooling surroundings, not heating them. That alone renders the concept that melting ice causes volcanism rather than vice-versa a bit counterintutitve. I would think there are enough examples of alpine glaciers melting prior to eruptions (from increased heat flow from rising magma) to show that cause-effect relationship.
On a global level, volcanism can cause significant atmospheric ash and sulfide levels which can decrease insolation and cause large scale cooling, but again, when the ash settles locally, there is a sufficient albedo change to cause the upper layers of the ice to absorb more heat rather than less, unless the thickness of pyroclastic material is great enough to act as an insulator, a phenomenon often observed in the spring at this latitude with wind-blown sediment, where ice can be preserved into late spring and early summer under a layer of dirt--especially in naturally shaded areas.
For this reason, much like with CO2, I think the researchers may have taken a trailing indicator and attributed causation to it.
I wouldn't argue there isn't some internal heat being generated by a nuclear reaction process. I just don't see evidence to support such a process on a massively large enough scale, and one lasting eons that would be needed to cause the amount of change the Earth's geology indicates has occurred throughout its history.
I agree with you on the remainder. I'm trying to better understand how a frozen dry world sitting on top of well insulated heat source, goes about becoming unfrozen in roughly 12K years. Determining how this happens is difficult.
I would imagine heating of the oceans plays a much larger role than heat transfer beneath the continents.