Motorized Wheel Chair Source

1st >>>you'll be properly treated
2nd>>> confidentiality is a must in the medical profession except towards an insurance co.
3rd >>> hospitals are government owned and clinics are privately owned.
4th >>>not all hospitals/clinics work directly with the insurance companies especially not the private clinics. You will have to foot the bill first and get your money back from your insurance company later on.

I speak out of experience as I am a Belgian expat and have been on medical insurance for over 30 years. When I visit a doctor/clinic in Belgium, I have to pay the bill first, send all the papers to my insurance co to get reimbursed. Hospitals ask for a written consent from your insurance that they agree to foot the bill. In any case, the reimbursement has always been done without any hassle (we've had different medical insurances over the years)
5th >>> if you follow point 4, you' ll realize you won't be able to keep some info out of your file unless you specifically ask the doctor to do so which, in my modest opinion, he won't do if the info is really relevant.
6th >>> when you have an insurance, the hospital or clinic will either ask your insurance's consent or, like I said before, you'lll have to pay first so you will - in both cases - have to seek consent from them in case of accident or in case you have to stay in a hospital or receive some special tests before the hospital will start on them.
Anyway, what do you have to hide if you have an accident?? unless... you have some undisclosed disease or a certain familial medical history that you haven't declared yet to your insurance.

Remain positive! Nothing will happen to you but it is better to be safe than sorry.
I wish you well and enjoy an excellent time in Belgium.

Edit :
reference to Kim's comments (sorry for what happened to her) :
You can not be repaid for your medical expenses by 2 or more insurance companies because
1st it wouldn't be honest
2nd you have to deliver the original bills to your insurance to be reimbursed.
In more than 30 years, never once, did our insurances refuse to repay us. You have to make sure to choose one that has a solid & honest reputation and read between the lines before you sign your contract as some medical insurances do not repay the travel expenses OR they'll repay only X % of your total medical expenses OR they'll repay your medical bills only up to the amount you would have paid in your own country. Be vigilant. Good luck!