If they don’t they will soon since you have to state who your insurer is on your taxes (part of Obamacare). I think the issue is more about getting on a enemies list as part of the snooping then being denied care in some way (that may be quite subtle).
They want to be able to withdraw right from your account.
Remember...they have access to all seniors on SS and disability folks....
They want access to bank accounts for EVERYONE.
They'll have to mine for non interest bearing accounts which aren't reported on your Income Tax.