Gallistel, Hesslow (PI of ferret study, [0]) and colleagues constitute the second, relatively smaller, group of neuroscientists who believe synapses are only an "effect" that one sees as a result of learning. The true mechanisms are either hidden in the nucleus, cell membrane or somewhere inside the cell [1]. This group so far has only very few substantially convincing experiments and more hypotheses. The ferret study [0] is one such experiment in this direction which was published in 2015. I am not aware of any more data to prove any of the hypothesis.
But of course even the inherent mechanisms that guide synapse formation and alteration are in the end guided by proteins "inside" the neuron. To me it seems these two groups are looking at the same idea at different steps of the memory learning pipeline.
[0] https://www.pnas.org/content/112/45/14060 [1] https://arxiv.org/ftp/arxiv/papers/2101/2101.09774.pdf