Yes. As a kid I mowed the yard of a rent house down the street a few times. Unbeknownst to me they reported to the IRS and my dad didn't. Time passes, IRS sent my dad a bill for more than what I earned mowing that yard.
https://www.irs.gov/taxtopics/tc756
In addition, if they made less than their standard deduction, there would also be no income tax liability or filing requirement.
What probably happened was that the kid was incorrectly sent a 1099 form. This is wrong for two reasons. First, it's not needed for a personal residence or rental properties for investment, only for businesses. Second, a household employee is not a contractor, and should generally receive a W-2 (or nothing at all, in the kid's case).