3) is wrong. The amplifiers are powered by DC, but one side of the fiber provides positive voltage and the other negative - the ocean is not a part of the circuit.
If nothing else, both ends still share a common ground reference, yeah?
https://pdfs.semanticscholar.org/3c72/998ffe9c39a1aa4a9faba4...
Edit: thinking about this more, it seems quite obvious that you need a current return path regardless. If it's not the ocean/earth - what is it?
Thanks!