The Profile Explanations/Special Circumstances section at the end of the form is the place to make special note of things like this.
That instruction deals only with assets that are considered to be owned by a parent but have been titled in the name of a child (including any siblings). It’s less common now, but under older tax laws it was a often the case that a parent would stash parent assets in a “child’s account or investment” in order to receive more favorable tax treatment. Changes to the kiddie tax have greatly reduced this practice.
On page 23 of the linked Profile instructions, parent investments are covered. 529 plans are explicity referred to as being properly reported as a parent asset, but there is no distinction made between a 529 account owned by a parent, owned by the student, or owned by someone else when the student is named as the beneficiary. A 529 account that is legitimately owned by the student (not a parent trying to disguise parent assets as belonging to someone else) should, in my opinion, be reported on Profile as a student asset, unless a college financial aid office specifically instructs otherwise in accordance with that school’s policy. FAFSA does not require reporting like this; instead, FAFSA explicitly directs that student-owned 529 accounts should be reported as a parent asset.
For a high school senior who will be sending Profile to a number of schools, my recommendation would be to report a 529 that is legitimately owned by the student as a student asset, and note in the explanation section how many dollars reported as a student asset/investment are in a student-owned 529. In subsequent years, after the student has selected a college to attend, ask the financial aid office what the school’s policy is on calculating the student’s EFC when a student-owned 529 is involved, and how the school would like that asset to be reported on Profile (as a parent asset or as a student asset).