If your income is so low that your tax liability would either be zero, or less than the $3,000 non-refundable tax credit, then you wouldn't be entitled to the whole $3,000 credit.
What happens in April each year is a settlement between what you have paid them, and what you should have paid them. Overpaying doesn't change what you should have paid them. Underpaying only impacts what you should have paid if it exposes you to interest and penalties.
The fact you are getting a refund in April is different from the refundable status or non-refundable status of a tax credit.
If a married couple with no kids has only $15,000 in income, which is less than the $24,000 standard deduction, then they have no tax liability. This makes them ineligible for non-refundable tax credits.
Congress is very careful about this point because it can determine who can and who can't benefit from the tax credit.