A great many of those 50% only realize they have no Federal Tax burden
after they file, and get back whatever tax had been withheld along with
any refundable credits.
In other words, anyone qualifying for a Health Care credit would need to
file a return to get it.
No, your understanding is not correct.
Even if there really are "50% of Americans who do not pay Federal Income
Tax", why would you assume that every one of them is also going to
qualify for premium assistance (aka subsidy)? For starters, many of
those may already be covered through an employer.
According to my tax research service, people who need coverage will
apply for insurance through the exchange beginning this October, and at
that time, information about family size, household income, and federal
poverty level (FPL) is combined to determine if eligible for a subsidy.
Household income projection for 2014 will be made using 2012 tax
return info and/or other info provided directly by applicant.
To your specific question, the subsidy, if the insured is eligible, will
be advanced directly to the QHP (qualifying health plan), so it will not
go through the insured's hands.
When they file their actual 2014 tax return, the income projection will
be reconciled with actual income to determine if they got too much
premium assistance, or not enough. Those who got too much will have to
pay it back, those who were eligible for more will get a refundable
credit. So these folks will be required to file a tax return, not to
receive a subsidy, but only to "true up" (reconcile) the projection with
actual and settle the difference.