If they send a corrected one with your parents names instead of yours (then 2 of them one removing the income from you and 1 for your parents) then no you have to do nothing.
If they won't correct it, you have to issue one to your parents and report it as the IRS will be looking for it regardless that you became the nominee, you just also create a negative amount to offset the 1099.
If ever audited, you will say I was just acting as agent for my aging parents and the money was theirs.
Thinking of another thing you could do is deposit monies in a joint bank account with your parents and yours names... The money goes in so they received it. Any money that is used for rental is their rental expense then. You could have a legal agent agreement whereby you get 15% of all rent (that is arms length) , this would then have you recording taxable income as self-employment and them being able to use it as a management fee). Or any gifting can be done from this same account , not as you as agent if you don't want to create taxable income. Just make sure, however you do it that if you decide to be their legal agent, you document it with legal agreements.
**I don't work for TT. Just trying to help. All the best.
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**Mark the post that answers your question by clicking on "Mark as Best Answer" I am NOT an expert and you should confirm with a tax expert.
