Not necessarily. I believe some Europeans (eg Scandinavians and yes Americans) can sometimes have some worldwide cover from their home countries, worth it's weight in gold if it provides comprehensive cover. Maybe these are all courtesy of their former employment. Other that that I would expect that you are correct.... go see an insurance broker when you get here.
Over 75 years you can have cover, but that cover will usually be with a company you were with prior... they limit new customers to a certain age. But it is an expensive item some forego. Many 'self insure', ie keep a healthy bank balance to cover eventualities. Certain Visa types actually require this too, a healthy maintained bank balance, that actually you are not meant to spend on anything oddly enough. There is also a visa class that requires medical insurance... both of these associated with what is called a retirement extension, how many live here. Another topic.......