That's correct, if you're amending to claim a refund.
According to Time for filing a claim for refund in the IRS' Publication 17:
Generally, you must file your claim for a credit or refund within 3 years after the date you filed your original return or within 2 years after the date you paid the tax, whichever is later. Returns filed before the due date (without regard to extensions) are considered filed on the due date (even if the due date was a Saturday, Sunday, or legal holiday). These time periods are suspended while you are financially disabled, discussed later.
If the last day for claiming a credit or refund is a Saturday, Sunday, or legal holiday, you can file the claim on the next business day.
If you don't file a claim within this period, you may not be entitled to a credit or a refund.
If you're amending and not claiming a refund, you can file beyond that time period. The government is happy to take the money owed.
Since you're amending after the original due date of the return, and you'll owe money, the IRS will process your amended return and send you a notice for any penalties and interest that are due.
Amended return policies for states are generally fairly close to the IRS', but their terms may vary.
