If you have doubt the claim that you do not need any paperwork to be able to get the visitors health insurance that you need to travel out, then you need to change your mind. This is a very true claim and no one should bug you with so much paperwork before you are granted the insurance that you need. Of course, there is the little personal information that you would need to be able to get the cover.
You will need to give your full names, your next of kin information, your date of birth and that of your next of kin as well so that your insurance is processed. You will not need any other bulk paperwork for the process to complete and also you will not need to give any medical test results for this insurance.
It is quite simple and direct. However, you may need to compare the different plans to be able to identify the one which you would want to have. It would pay you a lot when you take your time to ensure that you have the right one. Matters of insurance are quite sensitive and tricky and so you may need an expert to guide you.
You may also need to find out the possibility of getting trip cancellation insurance just in case things change or your trip is interrupted when you least expected, there should be someone to reimburse you.