cj, that's it exactly. The standards for a certified charger (eg UL, cUL, CSA, etc) require isolation. So the discussion stems from the opinions on whether to add a ground jumper from the supply side of the charger to the output side. Many diagrams, including some from ABYC show such a ground jumper. However, all these diagrams show the ground jumper to the DC negative connecting to the boat's isolated ground, not the shorepower ground. So, if you intend to add the ground jumper, do it only from an isolated ground derived from either an isolation transformer or a ground isolating device.
Most transformers are typically called isolation transformers as most have no connection between the input and output windings as there is in an "autotransformer". However, the particular type of transformer that complies with the standards for chargers usually has a grounded metal foil or shield between the primary and secondary windings. The intention is of course that should either winding fail, there's no way that the primary voltage can leak across the barrier and enliven the secondary with an overvoltage. Other types of isolation barriers are sometimes acceptable subject to rigorous testing.
- Grandad