Absolutely incorrect if you reside outside of IoM or CI and are aiming to open an offshore account. If you wanted to open an onshore account at a local bank over there then, yes, you would need to be a resident there and would need to prove local residency.
Yes, my imprecision, I apologize.
A non-resident can indeed open a new offshore account in these jurisdictions on the proviso that a substantial opening deposit is made, and a significant balance is retained.
As suggested earlier, offshore banking is largely a quest to sign-up customers with a high net worth and keep them hooked up to their bespoke milking machines.