Both statements are a lie, of course; and the OP fails as a false comparison fallacy, one issue having nothing to do with the other.
No one is 'required' to 'prove' he has health insurance, opting to pay the tax instead.
And undocumented immigrants are indeed required to prove they're authorized to enter the country, or have a good cause claim for refugee status; lacking either will result in being deported.
The ignorance and stupidity of most on the right knows no bounds.
>"No one is 'required' to 'prove' he has health insurance, opting to pay the tax instead."
You can sugar cote it all you want, but if you don't have an insurance, you're not opting to pay, you're forced to pay a tax/penalty.