The statement you quoted is not really correct. For one, taxing Greek owned ships will not change flagging in any way. There is nothing now in place stopping ships that are owned by a Greek or any other company from flying whatever flag they choose. The one general exception is for ships operating in cabotage (i.e domestic service). A quick look at the fleet of Greek owned Danaos bears this out: there are ships with flags from Malta, Cyprus, Panama and Liberia but none from the sample I looked at with a Greek flag. Some of the generally richer countries offer financial or tax incentives to maintain some semblence of a domestic fleet in case of emergency or for pride but as far as I know, there are no legal restrictions in place that would keep the ship's owner from changing flags at their convenience.

Flag choice will have little if any impact on insurance rates. No matter the flag, a ship owner can easily under-insure a ship, especially for old junkers hauling non-hazardous (bulk) cargo. It's their risk after all, plus tracing actual ownership can be very difficult if not impossible. For older ships, this option can be very attractive. Far more important to insurers is where (actually with whom) the ship is classed. The use of a reputable classification society (Lloyd's, American Bureau of Shipping, Det Norske Veritas...) will do much more to impress insurers than the flag on the stern.

Flag choice will impact inspections. Increased inspections by the three major Port State Control organizations (Tokyo MOU, Paris MOU and the US Coast Guard) will result in lower ship productivity and there will be greater uncertainty for a shipper but the major benefit is low crewing requirements/costs. Note also that the relationship between flags and their performance rating is not necessarily intuitive. Simply being European doesn't help the Belgians who are currently targeted by the Coast Guard and in the gray area for Tokyo MOU. Meanwhile, the Marshall Islands and Liberia are white (i.e. not targeted) for both of the MOU's and also non-targeted by the Coast Guard.

Regardless of the ship's classification or flag, I agree with the quote from the ship owner, good luck tracking these guys down now to make them pay taxes. For this tax to have been effective, they would have had to establish it quickly and without the ship owners' prior knowledge. Forget it now.