As to "the certain type of insurance" - there's no legal requirement, I suspect they may just be commenting on the fact that a lot of standard travel insurance policies don't cover cycling.
Really?? I don't know about buying travel insurance coming to America, but both my standard (most expensive country) medical insurance and the travel policies I've looked into for European travel Just Cover medical expenses -- plane, train, bike, falling down, you name it. They'll try to get reimbursed from the airline or train companies, or the restaurant with the slippery stairs, if there were an accident, I'm sure.
As an example, my medical insurance covered costs for me in the ER when I was hit by a car; Blue Cross then sent the bills to the driver's insurance company (who paid promptly for a car insurance company!).